What is the definite integral of x^2/(x^2+1) from 1 to 0 ?

1 Answer
May 4, 2018

int_1^0 =pi/4-1=-0.2146018366

Explanation:

Starting out with the integral,

int_1^0 x^2/(x^2+1) dx

We want to get rid of x^2,

int_1^0 ((x^2+1)/(x^2+1)-1/(x^2+1)) dx

int_1^0 (1-1/(x^2+1)) dx

=> int_ 1 dx - int_ 1/(x^2+1)dx

Which gives,

x-arctan(x)+C

pi/4+(-x)|_0^1 => pi/4-1=-0.2146018366

This was a kinda strange integral since it goes from 0 to 1. But, these are the calculations I got to.