" 7."int_(0)^( pi/4)sqrt(tan theta)d theta

Show that int_(0)^(pi//4) sqrt(tan theta) d theta = (1)/(sqrt(2)) log(sqrt(2)-1)+(pi)/(2sqrt(2))

int_(0)^(pi) sqrt(2-2cos theta) d theta

Evaluate int_0^(pi/4)sqrt(1+tan^2theta)d theta.

Evaluate int_(0)^(pi//4) log (1+tan theta)d theta

Evaluate int_(0)^(pi//4) log (1+tan theta)d theta

STATEMENT 1: int_(0)^((pi)/(4))log(1+tan theta)d theta=(pi)/(8)log2 STATEMENT 2:int_(0)^((pi)/(2))log sin theta d theta=-pi log2

int_(0)^((pi)/(4))tan^(3)thetad theta

int_(0)^( pi)sin theta d theta =

Prove that int_(0)^( pi/2)log(tan theta+cot theta)backslash d theta=pi log2