" 14."int_(0)^( pi/4)log(sin2 theta)d theta=(pi)/(4)log((1)/(2))

int_(0)^(10)log(1+cot theta)d theta=(pi)/(8)log2

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)(sin4theta)/(sintheta)d theta=0

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

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

If int_(0)^( pi/2)log sin xdx=k, then the value of the definite integral int_(0)^( pi/4)log(1+tan theta)d theta( i) -(K)/(8)( ii) -(K)/(4) (iii) (K)/(8) (iv) (K)/(4)

int_(0)^((pi)/(4))log sin2xdx equals to

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

Prove that, int_(0)^(pi)log(1+cos x)dx=-pi log2 , given int_(0)^((pi)/(2))log((sin x))dx=(pi)/(2)"log"(1)/(2) .

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