# Integral calculator

Wolfram Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals. It also shows plots, alternate forms and other relevant information to enhance your mathematical intuition.

Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral. Get immediate feedback and guidance with step-by-step solutions and Wolfram Problem Generator.

The indefinite integral ofdenotedis defined to be the antiderivative of. In other words, the derivative of is. Since the derivative of a constant is 0, indefinite integrals are defined only up to an arbitrary constant. For example, since the derivative of is. The definite integral of from todenotedis defined to be the signed area between and the axis, from to.

Both types of integrals are tied together by the fundamental theorem of calculus. This states that if is continuous on and is its continuous indefinite integral, then. This means. Sometimes an approximation to a definite integral is desired. A common way to do so is to place thin rectangles under the curve and add the signed areas together. Wolfram Alpha can solve a broad range of integrals. Wolfram Alpha computes integrals differently than people. It calls Mathematica's Integrate function, which represents a huge amount of mathematical and computational research.

Integrate does not do integrals the way people do. Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes. One involves working out the general form for an integral, then differentiating this form and solving equations to match undetermined symbolic parameters.

Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica's strong algebraic computation capabilities to solve.

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Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.

While these powerful algorithms give Wolfram Alpha the ability to compute integrals very quickly and handle a wide array of special functions, understanding how a human would integrate is important too. As a result, Wolfram Alpha also has algorithms to perform integrations step by step.This website uses cookies to ensure you get the best experience.

By using this website, you agree to our Cookie Policy. Learn more Accept. Definite Integrals.

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Conic Sections Trigonometry. Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Definite Integral Calculator Solve definite integrals step-by-step.

Correct Answer :. Let's Try Again :. Try to further simplify.

## Definite Integral Calculator

In the previous post we covered integration by parts. Quick review: Integration by parts is essentially the reverse Sign In Sign in with Office Sign in with Facebook. Join million happy users!

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User Data Missing Please contact support. We want your feedback optional. Cancel Send. Generating PDFWolfram Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals.

It also shows plots, alternate forms, and other relevant information to enhance your mathematical intuition. Enter your queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral. Since the derivative of a constant is zero, indefinite integrals are defined only up to an arbitrary constant.

Both types of integrals are tied together by the fundamental theorem of calculus. Sometimes an approximation to a definite integral is desired.

A common way to do so is to place thin rectangles under the curve and add the signed areas together. Wolfram Alpha can solve a broad range of integrals. Wolfram Alpha computes integrals differently than people.

It calls Mathematica 's Integrate function, which represents a huge amount of mathematical and computational research. Integrate doesn't do integrals the way people do.

Instead, it uses powerful, general algorithms that often involve very sophisticated math. There are a couple of approaches that it most commonly takes.

One involves working out the general form for an integral, then differentiating this form and solving equations to match undetermined symbolic parameters.

Even for quite simple integrands, the equations generated in this way can be highly complex and require Mathematica 's strong algebraic computation capabilities to solve. Another approach that Mathematica uses in working out integrals is to convert them to generalized hypergeometric functions, then use collections of relations about these highly general mathematical functions.

While these powerful algorithms give Wolfram Alpha the ability to compute integrals very quickly and handle a wide array of special functions, understanding how a human would integrate is important too. As a result, Wolfram Alpha also has algorithms to perform integrations step by step. These use completely different integration techniques that mimic the way humans would approach an integral. This includes integration by substitution, integration by parts, trigonometric substitution, and integration by partial fractions.

To see full output on this page you need to enable JavaScript in your browser. More than just an online integral solver Wolfram Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals.

Tips for entering queries Enter your queries using plain English. What are integrals? Integration is an important tool in calculus that can give an antiderivative or represent area under a curve. How Wolfram Alpha calculates integrals Wolfram Alpha computes integrals differently than people.This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy. Learn more Accept. Definite Integrals.

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Conic Sections Trigonometry. Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Definite Integral Calculator Solve definite integrals step-by-step. Correct Answer :. Let's Try Again :. Try to further simplify.

### Evaluate an Integral

Advanced Math Solutions — Integral Calculator, trigonometric substitution. In the previous posts we covered substitution, but standard substitution is not always enough. Integrals involving In the previous post we covered integrals involving powers of sine and cosine, we now continue with integrals involving Sign In Sign in with Office Sign in with Facebook.

Join million happy users! Sign Up free of charge:. Join with Office Join with Facebook. Create my account. Transaction Failed! Please try again using a different payment method.

Subscribe to get much more:. User Data Missing Please contact support. We want your feedback optional. Cancel Send. Generating PDF See All implicit derivative derivative domain extreme points critical points inverse laplace inflection points partial fractions asymptotes laplace eigenvector eigenvalue taylor area intercepts range vertex factor expand slope turning points.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! For more about how to use the Integral Calculator, go to " Help " or take a look at the examples.

Enter the function you want to integrate into the Integral Calculator. 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. In " Examples"you can see which functions are supported by the Integral Calculator and how to use them. When you're done entering your function, click " Go! 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.

Clicking an example enters it into the Integral Calculator. Moving the mouse over it shows the text. 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. Not what you mean? Use parentheses! Set integration variable and bounds in " Options ". An extremely well-written book for students taking Calculus for the first time as well as those who need a refresher.

This book makes you realize that Calculus isn't that tough after all. Paid link. As an Amazon Associate I earn from qualifying purchases. 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.This website uses cookies to ensure you get the best experience.

By using this website, you agree to our Cookie Policy. Learn more Accept. Conic Sections Trigonometry. Conic Sections. Matrices Vectors. Chemical Reactions Chemical Properties. Integral Calculator Integrate functions step-by-step. Correct Answer :. Let's Try Again :. Try to further simplify.

Integration by parts is essentially the reverse of the product rule. It is used to transform the integral of a In the previous post we covered common integrals click here.

There are a few more integrals worth mentioning Sign In Sign in with Office Sign in with Facebook. Join million happy users! Sign Up free of charge:. Join with Office Join with Facebook. Create my account. Transaction Failed! Please try again using a different payment method.Enter an expression below to find the indefinite integral, or add bounds to solve for the definite integral.

Make sure to specify the variable you wish to integrate with. To get started, try working from the example problem already populated in the box above. Just click the blue arrow and you'll see a solved example. Modify that expression as needed. A few examples of solved integrals are provided below as well.

These are the types of problems you can solve with this tool. Remember, these solvers are great for checking your work, experimenting with different equations, or reminding yourself how to work a particular problem. Maybe you just need a quick answer at work and don't want to solve the problem by hand. But if you're working on homework your teacher is going to want to see how you solved the problem step-by-step to make sure you understand the process.

It's not just about getting the right answer afterall, a computer can do that!

### Integral Calculator

So, consider going back to our list of calculus lessons to review. You might be looking for other lessons that cover integrals and integration to help further understand what the tool above is actually doing. After all, it does you no good to simply have the answer unless you know it's right and why it's right!

Step 1: Enter an expression below to find the indefinite integral, or add bounds to solve for the definite integral. Step 2: Click the blue arrow to compute the integral. More Information To get started, try working from the example problem already populated in the box above.