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Definite Integral Calculator
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Definite Integrals are the integrals calculated between the fixed intervals.

Definite Integral Calculator is an online tool which is used to calculate the value of integral covering the selected interval. For using this calculator, you need to specify the integral and the specific value for which integral has to be done.

Below is given a default function with its upper and lower limit, click "Submit". First, it will integrate the function and then limits are evaluated by finding the difference between them to give the value of definite integral.

 

Steps for Definite Integrals Calculator

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Step 1 :  

Observe the given function and limits.



Step 2 :  

Apply the formula: $\int_{a}^{b}$ f(x) dx = F(b) - F(a)


Where, F(a) = lower limit value of the integral


and F(b) = upper limit value of the integral.



Examples on Definite Integrals Calculator

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  1. Solve the definite integral  $\int_{2}^{4}$ (x + 5) dx ?


    Step 1 :  

    Given function = (x + 5) and upper limit = 4 and lower limit = 2



    Step 2 :  

    $\int_{2}^{4}$ (x + 5) dx = $\int_{2}^{4}$ x dx + 5 $\int_{2}^{4}$ (1) dx


    => $\frac{4^{2}}{2}$ + 5(4) - $\frac{2^{2}}{2}$ + 5(2)


    => 8 + 20 - (2 + 10)


    => 8 + 20 - 2 - 10


    => 16



    Answer  :  

    16



  2. Solve the definite integral  $\int_{1}^{3}$ x3 dx ?


    Step 1 :  

    Given function = x3 and upper limit = 3 and lower limit = 1



    Step 2 :  

    $\int_{1}^{3}$ x3 dx


    => $\frac{3^{4}}{4}$  - $\frac{1^{4}}{4}$


    => $\frac{81}{4}$  - $\frac{1}{4}$


    => $\frac{81 - 1}{4}$


    => $\frac{80}{4}$


    => 20



    Answer  :  

    20



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