Definite Integral Calculator

Created By : Abhinandan Kumar

Reviewed By : Rajashekhar Valipishetty

Last Updated : Apr 15, 2023

Free online Definite Integral Calculator tool computes the definite integral of a function over an interval using numerical integration. Give the variable range as the input and get the instant output in no time.

Function f(x)
Intervals
 

Definite Integral Calculator: Do you feel Definite Integral calculations is difficult?. Not anymore with our easy tool, this calculator gives the answer along with the detailed explanation for the given function range. It makes your calculations easier and quick for the given inputs.

Steps to Find Definite Integral

Follow the below given step by step procedure to check the definite integral of a function within the range. These are the simple steps helpful for you to calculate the integral.

  • Calculate the antiderivative of a function f(x)
  • Take the range values a & b. Find the f(a), f(b)
  • Subtract f(b) from f(a) to get the definite integral of a function in the specified range

The mathematical representation of Definite Integral is

Integration a to b f(x)dx = [F(x)]b to a = F(b)-F(a)

Where F(x) is an antiderivative of f(x)

F(x)= Integral f(x)d(x)

Example:

Question. Calculate the Definite Integral of the function f(x) = x – 1, on the interval [1, 10]?

Answer:

F(x)=∫(x−1)dx=x2/2-1

By substituting the 10 and 1 in the place of x

F(10)= (100/2)-1= 50-10= 40

F(1)= (½)-1= 0.5-1= -0.5.

F(10)-F(1)= 40-(-0.5)= 40.5

Frequently Asked Questions on Definite Integral

1. What is the Definite Integral?

Definite integral is an integral having both upper and lower limits. It is also known as Riemann integral. The definite integral of a function represents the area under the curve function from the lower limit to upper limit. The value of an integral function is conveyed as the difference between the integral of the upper and lower limits of the independent variables.

2. Can a Definite Integral be negative?

Yes, a definite integral can be negative.

3. Can we multiply the definite integrals?

No, you cannot multiply the definite integrals. The reason is integrals are functions.

4. What are the two types of integrals in Maths?

The two different types of integrals are Definite Integrals and Indefinite Integrals.

5. What is the difference between the definite and indefinite integral?

Definite Integral and Indefinite Integral are the opposite in their properties. Definite Integral contains lower and upper limits, represents the area under the curve of a function from lower to upper limit. DI does not have the constant integration. Indefinite integral offers the answer to the differential questions. It is not having upper and lower limits. It has a constant integration.