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" prove that "int(0)^( pi/2)log(sin thet...

" prove that "int_(0)^( pi/2)log(sin theta)d theta=(-r pi)/(2)log2

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int_(0)^( pi/2)sin^(2)theta d theta=

int_(0)^( pi/2)sin^(2)theta d theta=

int_(0)^( pi/2)sin^(3)theta d theta=

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

Show that int_(0)^((pi)/(2))log(sin2x)dx=-(pi)/(2)(log2)

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

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