Question

`int_(0)^(1) (x^(2))/(1+x^(2))dx` is equal to
A. `pi/4-1`
B. `1-pi/2`
C. `pi/2-1`
D. `1-pi/4`

Answer 1

Correct Answer - D
`int_(0)^(1)(x^(2))/(1+x^(2))dx=int_(0)^(1)(1+x^(2))/(1+x^(2))dx-int_(0)^(1)(1)/(1+x^(2))dx`
`= int_(0)^(1)1dx - int_(0)^(1)(1)/(1+x^(2))dx`
` = [x]_(0)^(1)-[tan^(-1)x]_(0)^(1)=1-(pi)/(4)`