Definite Integral Calculator

Definite Integral Calculator is used to compute the value of a definite integral. In integral calculus, a definite integral is defined as an integral that has a definite value.

What is a Definite Integral Calculator?

Definite Integral Calculator is an online tool that helps to integrate the given function between the specified upper and lower limits. Definite integrals are used to calculate the area under a curve. To use the definite integral calculator, enter the values in the given input boxes.

Definite Integral Calculator

NOTE: Upper limit should always be greater than the lower limit.

How to Use Definite Integral Calculator?

Please follow the steps given below to find the value of the definite integrals using the online definite integral calculator:

• Step 1: Go to Cuemath's online definite integral calculator.
• Step 2: Enter the values in the given input boxes of the definite integral calculator
• Step 3: Click on the "Calculate" button to integrate the given function.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

How Does Definite Integral Calculator Work?

Integration can be thought of as the process of adding infinitesimal area strips to get a whole. Further, it is the inverse process of differentiation. There are two types of integrals - indefinite and definite. Indefinite integrals do not have any specified limits. Hence, the final value is indefinite in nature. Definite integrals are used to find the area under a curve between two endpoints. The limits of the definite integral act as endpoints. Thus, the lower limit denotes the starting point of the integration. Similarly, the upper limit represents the ending point of the integration. The steps to solve a definite and an indefinite integral are the same. The only difference is that in a definite integral we apply the limits to find a definite value of the function. The steps to perform integration are as follows:

• Let the function be given as \(\int_{a}^{b} f(x)dx\). Here, a is the lower limit and b is the upper limit.
• Integrate the function by using any of the methods. (Substitution, by parts, partial fractions, and decomposition methods). Thus, \(\int_{a}^{b} f(x)dx\) = \([F]_{a}^{b}\)
• Now apply the limits as F(b)−F(a).
• Solve the given expression to find the value of the definite integral.

Solved Examples on Definite Integrals

Example 1: Find the value of \(\int_{1.2}^{4.5} x^{3}dx\) and verify it using the online definite integral calculator.

Solution:

\(\int_{1.2}^{4.5} x^{3}dx\) = \(\left [ \frac{x^{4}}{4} \right] _{1.2}^{4.5}\)

= \(\left [ \frac{4.5^{4}}{4} \right] - \left [ \frac{1.2^{4}}{4} \right]\)

= 102.

Example 2: Find the value of \(\int_{2}^{3}sinxdx\) and verify it using the online definite integral calculator.

Solution:

We solve this integral by using integration by parts.

\(\int_{2}^{3}sinxdx\) = \(\left [ -cosx \right] _{2}^{3}\)

= - cos(3) - (-cos (2))

= 0.57

Similarly, you can use the definite integral calculator to find the value of integrals for the following:

• x³ / 2 for limits x = 2.3 to x = 5
• xsinx for limits x = -1 to x = 2

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