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

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Answer 1 · 2018-05-04T18:34:15

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

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.