`int_0^(pi/2)x^2c o s e c^2x dx=pilog2`

int_0^(pi//2) x^2 cos 2x dx

int_0^(pi/2) sin x sin 2x dx

int(sec^2x)/(c o s e c^2x)dx

int_0^(pi/2) e^(sinx).sin 2x dx =

int_0^(pi//2) cos x e^(sin x) dx is :

Prove that int_0^(pi//8) log |1 + tan 2x|\ dx = pi/16 log_e 2.

int_0^(pi/2) e^x dx is equal to

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)dtheta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin"thetadtheta"=-pilog2.

STATEMENT 1: int_0^(pi/4)log(1+t a ntheta)d theta=pi/8log2. STATEMENT 2: int_0^(pi/2)logsin theta d theta =-pilog2.

(i) int_0^(pi//2) cos x dx (ii) int_(-pi//2)^(pi//2) cos x dx (iii) int_0^(pi//2) cos 2x dx