Definite Integral Calculator

Integration is a method of finding the area under the graph of a continuous function. Integrals are of two types, one being

Definite integral and the other being Indefinite integral. Definite integral calculator is an instant tool which makes the

calculations involving definite integral, very simple and fun.


Example 1: Find the definite integral value of the function, f(x) = 3x² – 2x + 1 from ‘x’ ranging from 0 to 2.

 According to thePower Rule: ∫xⁿ dx= x⁽ⁿ⁺¹⁾/ (n+1)


Applying the above formula for every term in the function, we get

 ∫(fx) dx = 3* x²⁺¹/(2+1) – 2* x¹⁺¹/(1+1) + 1*x

 ∫f(x)dx = x³ – x² + x

First substitute x=0 and then x=2 in the above answer.

When x=2 ∫f(x)dx=(2)³-(2)²+(2) = 6

When x=0 ∫f(x)dx=(0)³-(0)²+0= 0

Now subtract 2-0=2 Hence the definite integral of given f(x) is 2.


 
Example 2: Find the definite integral value of the function, f(x) = 3x³ - 4 from ‘x’ ranging from -1 to 1.

 ∫xⁿ dx= x⁽ⁿ⁺¹⁾/ (n+1)


Apply the above formula for every exponent in the function, we get

 ∫(fx) dx = 3* x³⁺¹/(3+1) – 4*x ∫f(x)dx = 3x⁴/4 – 4x

First substitute x=-1 and x=1 in the above answer.

When x=-1 ∫f(x)dx=3(-1)⁴/4 – 4(-1)= 3/4+4= 19/4

When x=1 ∫f(x)dx=3(1)⁴/4 – 4(1)= 3/4-4= -13/4

Now subtract 19/4 – (-13/4) = (19+13)/4= 32/4

 Hence the definite integral of given f(x) is 8.