Definite Integral Calculator


Please wait.. loading-icon

More Calculators

Introduction to Definite Integral Calculators

Definite integration calculator is an online tool to calculate integrals with limits online. It helps users to evaluate the area under the curve. Definite integrals are the contrasting values of the function f(x) given for the upper and lower bound values of any independent variable x.

For Instance,


There are two types of integrals one is definite integrals and the other one is indefinite integrals. The indefinite integrals may calculate by using the indefinite integrals calculator online. But here, integral calculator with limits help to compute the definite integral online.

What is a Definite Integral Calculator with Steps?

Integration calculator with limits are used for executing the limit and summation. And to find the net area between a function and the x-axis.

The definite integrals notation used by definite integral solver is:

$$ \int_a^b f(x) dx \;=\; f(x)|_a^b \;=\; f(b)-f(a) $$

It is traditional to use the square brackets in function to differentiate between two limits. A definite integral calculator is used to get the exact area under the curve.

While in indefinite integrals, the finding of integrals is also known as integration or integrating f(x). The function F is the integration of f for a real constant C. Here is the notation of indefinite integrals are:

$$ \int f(x) dx \;=\; F(x)+C $$

Here a point to be noted is that the notations of definite and indefinite integrals are almost similar. Just the difference is that definite integrals are divided into two limits.

Related: For the estimation of area of irregular shape, try our area under graph calculator

Formula used by the Integral Calculator with Bounds

The definite integral calculator with steps uses the following formula to calculate the integrals.

$$ \int_a^b f(x) dx \;=\; f(b)-f(a) $$

The definite integrals have two limits for a function f(x).

F(a) is the lower limit
F(b) is the upper limit

Let's understand the working of definite integral calculator with a manual example and its solution.

Example Solved By Integration Calculator with Limits

Consider we have a function:

evaluate definite integral online with steps

Let's integrate it as follow:

$$ \int_0^2 x^2 dx $$ $$ \int_0^2 x^2 dx \;=\; \Biggr[ \frac{x^3}{3} \Biggr]_0^2 $$ $$ \int_0^2 x^2 dx \;=\; \Biggr[ \frac{2^3}{3} - \frac{0^3}{3} \Biggr] $$ $$ \int_0^2 x^2 dx \;=\; \frac{8}{3} $$

Here "0" represents the lower limit and "2" represents the upper limit in the integrals with the corresponding x-axis. And in the definite integrals, we have to find the area of the curve, and for this purpose, we divide the curve into rectangles and then find the summation of these partitioned rectangles.

Importance of Using Definite Integral Solver

The integral calculator with limits calculates the single-variable function given the specific limits of the integration. This calculator helps the user to evaluate the different values of integration.

By using this online definite integral calculators with steps using this calculator, one can save a lot of/time. They don't have to manually spend a couple of hours doing these sums.

The evaluate definite integrals calculator also show plots, graphs, alternate forms, and other vital information to enhance their mathematical knowledge.

Just like a integral with bound values, our website also provides improper integral calculator for the calculation of improper integrand.

How does Definite Integration Calculator Work?

One can quickly get accurate results by using the following steps in a integral calculator with bounds. The steps to use definite integrals calculator are as follows:

  1. Firstly, upload your example/ function in the search bar.
  2. Now select the variable from x, y, and z coordinates.
  3. Select the value of upper in the given field.
  4. Select the value of the lower bound in the provided field.
  5. Now verify your values and equation from the preview whether it is correct.
  6. Hit the "CALCULATE" button on integral calculator with bounds to get the step by step evaluation of integration.

We also offers double integration calculator and triple integration calculator for solving integration twice or thrice.

Benefits of Using Definite Integral Calculator

Nowadays, technology is so advanced that students get so many advantages. Now students don’t have any need to solve complex problems manually. They need to learn some efficient clicks to avail the perks of available online websites.

Especially calculus always gives a tough time to students with its long and complex problems. So, students do not need to worry about the calculations and accuracy of their problems. This online definite integral calculator also provides you with one-click solutions.

As many online websites offer different tools for the methods of integration. Definite integral calculators also give so many advantages. You can quickly solve your complex problems here by following a few steps. By using definite integrals calculator, we have benefits like:

  1. Accuracy of the equation.
  2. Fast and reliable source.
  3. Easy in execution
  4. Relieve stress.
  5. Convenient and useful.

We hope this website is a great place for those who are doing their education in maths/calculus. We don't need to do calculation and paper pencil work here. No doubt, our website provide home of calculus tools like long division integral calculator and many more. So keep connect with us for happy learnings.

Frequently Asked Question

Define a Definite Integral and also Give an Example.

Definite integral is the area of the curve between two fixed limits that you can calculate on this definite integral solver.


$$ \int_0^2 x^2 dx \;=\; \frac{8}{3} $$

Can Definite Integral be Negative?

As definite integrals are the sums of the areas and the area is always positive definite integrals may be positive, negative, or zero.

Moreover, you can cross check by evaluating integrals on evaluate definite integral calculator with steps

What does Definite Integral Represent?

There are different coordinates, the definite integrals give the area of the function under the curve. There are limits, a represents the lower limit and b represents the upper limit.

Thus for the calculation of exact exact area under the curve, one may try this amazing integration calculator with limits.

What is the Definite Integral of a Constant?

The definite integral of any constant number will be "0" because the real number will never dependent upon any variable.

But if you feel any confusion then you can evaluate it using evaluate definite integral calculator on the top of this webpage.