Question

Evaluate :
(i) `int_(0)^(oo) (dx)/(e^(x)+e^(-x))`, (ii) `int_(0)^(1) (x)/(1+sqrt(x))dx` , (iii) `int_(0)^(pi//2) (sinxcosx)/(cos^(2)x+3cosx+2)`
(iv) `int_(0)^(pi/2) (sin2theta d theta)/(sin^(4)theta+cos^(4)theta)`, (v) `int_(0)^(pi//4) (sinx+cosx)/(9+16 sin 2x)dx`

Answer 1

Correct Answer - (i) `pi/4` , (ii) `5/3 - 2 ln 2` , (iii) `ln (9/8)` , (iv) `pi/2` , (v) `1/20 ln 3`