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Calculus Calculator

Get detailed solutions to your math problems with our calculus step-by-step calculator . practice your math skills and learn step by step with our math solver. check out all of our online calculators here .,  example,  solved problems,  difficult problems.

Here, we show you a step-by-step solved example of calculus. This solution was automatically generated by our smart calculator:

We can solve the integral $\int\cos\left(3x\right)dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $3x$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

 Intermediate steps

Differentiate both sides of the equation $u=3x$

Find the derivative

The derivative of the linear function times a constant, is equal to the constant

The derivative of the linear function is equal to $1$

Now, in order to rewrite $dx$ in terms of $du$, we need to find the derivative of $u$. We need to calculate $du$, we can do that by deriving the equation above

Isolate $dx$ in the previous equation

Substituting $u$ and $dx$ in the integral and simplify

Take the constant $\frac{1}{3}$ out of the integral

Apply the integral of the cosine function: $\int\cos(x)dx=\sin(x)$

Replace $u$ with the value that we assigned to it in the beginning: $3x$

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

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Integral Calculator

Calculate integrals online — with steps and graphing.

The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free!

Our calculator allows you to check your solutions to calculus exercises. It helps you practice by showing you the full working (step by step integration). All common integration techniques and even special functions are supported.

The Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions.

For more about how to use the Integral Calculator, go to " Help ". Also see " Examples ".

And now: Happy integrating!

Enter the function you want to integrate into the Integral Calculator. Skip the f(x)= part and the differential dx ! The Integral Calculator will show you a graphical version of your input while you type. Make sure that it shows exactly what you want. Use parentheses, if necessary, e.g. a/(b+c) . Write decimal fractions with a period instead of a comma, e.g. 3.141 .

In " Examples " you will find some of the functions that are most frequently entered into the Integral Calculator.

When you're done entering your function, click " Go! ", and the Integral Calculator will show the result below.

In " Options ", you can set the variable of integration and the integration bounds . If you don't specify the bounds, only the antiderivative will be computed.

Click an example to enter it into the Integral Calculator (the current input will be deleted).

Configure the Integral Calculator:

The practice problem generator allows you to generate as many random exercises as you want.

You find some configuration options and a proposed problem below. You can accept it (then it's input into the calculator) or generate a new one.

Calculate the Integral of … Enter your own Answer:

This will be calculated:

Use parentheses, if necessary. Also see " Examples ". Change integration variable and order in " Options ".

How the Integral Calculator Works

For those with a technical background, the following section explains how the Integral Calculator works.

First, a parser analyzes the mathematical function. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). In doing this, the Integral Calculator has to respect the order of operations . A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write 5x instead of 5*x . The Integral Calculator has to detect these cases and insert the multiplication sign.

The parser is implemented in JavaScript , based on the Shunting-yard algorithm , and can run directly in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. MathJax takes care of displaying it in the browser.

When the " Go! " button is clicked, the Integral Calculator sends the mathematical function and the settings (variable of integration and integration bounds) to the server, where it is analyzed again. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima .

Maxima takes care of actually computing the integral of the mathematical function. Maxima's output is transformed to LaTeX again and is then presented to the user. In many cases, the antiderivative is computed using the Risch algorithm , which is hard to understand for humans. That's why showing the steps of calculation is very challenging for integrals.

In order to show the steps, the calculator applies the same integration techniques that a human would apply. The program that does this has been developed over several years and is written in Maxima's own programming language. It consists of more than 17 000 lines of code. When the integrand matches a known form, it applies fixed rules to solve the integral (e.g. partial fraction decomposition for rational functions, trigonometric substitution for integrands involving the square roots of a quadratic polynomial or integration by parts for products of certain functions). Otherwise, it tries different substitutions and transformations until either the integral is solved, time runs out or there is nothing left to try. The calculator lacks the mathematical intuition that is very useful for finding an antiderivative, but on the other hand it can try a large number of possibilities within a short amount of time. The step by step antiderivatives are often much shorter and more elegant than those found by Maxima.

The "Check answer" feature has to solve the difficult task of determining whether two mathematical expressions are equivalent. Their difference is computed and simplified as far as possible using Maxima. For example, this involves writing trigonometric/hyperbolic functions in their exponential forms. If it can be shown that the difference simplifies to zero, the task is solved. Otherwise, a probabilistic algorithm is applied that evaluates and compares both functions at randomly chosen places. In the case of antiderivatives, the entire procedure is repeated with each function's derivative, since antiderivatives are allowed to differ by a constant.

The interactive function graphs are computed in the browser and displayed within a canvas element (HTML5) . For each function to be graphed, the calculator creates a JavaScript function, which is then evaluated in small steps in order to draw the graph. While graphing, singularities (e.g. poles) are detected and treated specially. The gesture control is implemented using Hammer.js .

If you have any questions or ideas for improvements to the Integral Calculator, don't hesitate to write me an e-mail .

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Calculus Problem Solver

This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

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Our math problem solver that lets you input a wide variety of calculus math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

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Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

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Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

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The calculus section of QuickMath allows you to differentiate and integrate almost any mathematical expression.

What is calculus?

Calculus is a vast topic, and it forms the basis for much of modern mathematics. The two branches of calculus are differential calculus and integral calculus.

Differential calculus is the study of rates of change of functions. At school, you are introduced to differential calculus by learning how to find the derivative of a function in order to determine the slope of the graph of that function at any point.

Integral calculus is often introduced in school in terms of finding primitive functions (indefinite integrals) and finding the area under a curve (definite integrals).

Differentiate

The differentiate command allows you to find the derivative of an expression with respect to any variable. In the advanced section, you also have the option of specifying arbitrary functional dependencies within your expression and finding higher order derivatives. The differentiate command knows all the rules of differential calculus, including the product rule, the quotient rule and the chain rule.

Go to the Differentiate page

The integrate command can be used to find either indefinite or definite integrals. If an indefinite integral (primitive function) is sought but cannot be found for a particular function, QuickMath will let you know. Definite integrals will always be given in their exact form when possible, but failing this QuickMath will use a numerical method to give you an approximate value.

Go to the Integrate page

The Fundamental Theorem of Calculus

Integrals were evaluated in the previous tutorial by identifying the integral with an appropriate area and then using methods from geometry to find the area. This procedure will succeed only for very simple integrals. The main result of this section, the fundamental theorem of calculus, includes a very important formula for evaluating integrals. This theorem shows us how to evaluate integrals by first evaluating antiderivatives. The theorem establishes an amazing relationship between the integral, which may be interpreted as an area, and the antiderivative, which is inversely related to the derivative; that is, it relates area and the derivative.

Let f be a continuous function on [a, b ], and define a function F by

The following theorem is called the fundamental theorem and is a consequence of Theorem 1 . The Fundamental Theorem of Calculus

0 = F (a) = G (a) + c

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Cover most of the math subjects in Algebra, and advanced Calculus for college students.

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How can type-in keys like e , z , a , and more.

• a , b , c , ..., x , y , z
• A , B , C , ..., X , Y , Z

What does the premium-pack offer

• Allows unlimited access to the problem solving server of FX Math Solver.
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What is the difference between FX Calculus Solver and FX Math Solver

• FX Calculus Solver is for college students, and FX Math Solver is mainly for high school students.
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• How do you solve word problems?
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• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
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• Middle School Math Solutions – Simultaneous Equations Calculator Solving simultaneous equations is one small algebra step further on from simple equations. Symbolab math solutions...

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The most rigorous math program you've never heard of.

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Math-M-Addicts students eagerly dive into complex math problems during class.

In the building of the Speyer Legacy School in New York City, a revolutionary math program is quietly producing some of the city's most gifted young problem solvers and logical thinkers. Founded in 2005 by two former math prodigies, Math-M-Addicts has grown into an elite academy developing the skills and mindset that traditional schooling often lacks.

"We wanted to establish the most advanced math program in New York," explains Ruvim Breydo, co-founder of Math-M-Addicts. "The curriculum focuses not just on mathematical knowledge, but on developing a mastery of problem-solving through a proof-based approach aligned with prestigious competitions like the International Mathematical Olympiad."

From its inception, Math-M-Addicts took an unconventional path. What began as an attempt to attract only the highest caliber high school students soon expanded to offer multiple curriculum levels. "We realized we couldn't find enough kids at the most advanced levels," says Breydo. "So we decided to develop that talent from an earlier age."

The program's approach centers on rigor. At each of the 7 levels, the coursework comprises just a handful of fiendishly difficult proof-based math problems every week. "On average, we expect them to get about 50% of the solutions right," explains instructor Natalia Lukina. "The problems take hours and require grappling with sophisticated mathematical concepts."

But it's about more than just the content. Class sizes are small, with two instructors for every 15-20 students. One instructor leads the session, while the other teacher coordinates the presentation of the homework solutions by students. The teachers also provide customized feedback by meticulously reviewing each student's solutions. "I spend as much time analyzing their thought processes as I do teaching new material," admits instructor Bobby Lee.

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Lee and the Math-M-Addicts faculty embrace an unconventional pedagogy focused on developing logic, creativity, and a tenacious problem-solving mindset over procedures. "We don't dumb it down for them," says Breydo. "We use technical math language and allow students to struggle through the challenges because that's where real learning happens."

Impressive results of Math-M-addicts students in selective math competitions highlight their ... [+] preparation and dedication.

For the Math-M-Addicts team, finding the right teachers is as essential as shaping brilliant students. Prospective instructors go through a rigorous multi-stage vetting process. "We seek passionate mathematical problem solvers first," says program director Sonali Jasuja. "Teaching experience is great, but first and foremost, we need people who deeply understand and enjoy the reasoning behind mathematics."

Even exceptional instructors undergo extensive training by co-teaching for at least a year alongside veteran Math-M-Addicts faculty before taking the lead role. "Our approach is different from how most US teachers learned mathematics," explains instructor Tanya Gross, the director of Girls Adventures in Math (GAIM) competition. "We immerse them in our unique math culture, which focuses on the 'why' instead of the 'how,' empowering a paradigm shift."

That culture extends to the students as well. In addition to the tools and strategies imparted in class, Math-M-Addicts alumni speak of an unshakable confidence and camaraderie that comes from up to several thousands of hours grappling with mathematics at the highest levels alongside peers facing the same challenges.

As Math-M-Addicts ramps up efforts to expand access through online classes and global partnerships, the founders remain devoted to their core mission. "Math education should not obsess with speed and memorization of math concepts," argues Breydo. "This is not what mathematics is about. To unlock human potential, we must refocus on cognitive reasoning and problem-solving skills. We are seeking to raise young people unafraid to tackle any complex challenge they face"

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Bibliometrics & citations, view options, recommendations, semi-analytical time differencing methods for stiff problems.

A semi-analytical method is developed based on conventional integrating factor (IF) and exponential time differencing (ETD) schemes for stiff problems. The latter means that there exists a thin layer with a large variation in their solutions. The ...

Two classes of implicit-explicit multistep methods for nonlinear stiff initial-value problems

The initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications. In order to reduce the computation cost, implicit-explicit (IMEX) methods are often applied to these ...

Continuous block backward differentiation formula for solving stiff ordinary differential equations

In this paper, we consider an implicit Continuous Block Backward Differentiation formula (CBBDF) for solving Ordinary Differential Equations (ODEs). A block of p new values at each step which simultaneously provide the approximate solutions for the ODEs ...

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