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

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Answer 1 · 2018-05-04T17:28:08

# 1-pi/4=1/4(4-pi)#.

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

#=int_1^0{(x^2+1)-1}/(x^2+1)dx#,

#=int_1^0{(x^2+1)/(x^2+1)-1/(x^2+1)}dx#,

#=int_1^0{1-1/(x^2+1)}dx#,

#=[x-arc tanx]_1^0#,

#=[1-arc tan1]-[0-arctan0]#,

#:. int_1^0x^2/(x^2+1)dx=1-pi/4=1/4(4-pi)#.