Question

How do you evaluate `intdx/(1+x^2)` from 0 to 1?

Answer 1

That is derivative of `tan^-1 x`, so

`int_0^1 dx/(1+x^2) = tan^-1 x]_0^1 = tan^-1(1)-tan^-1(0)`

`= pi/4 - 0 = pi/4`