" 9."int_(0)^( pi/2)cos xe^(sin x)dx

int_(0)^( pi/2)|cos x-sin x|dx

int_(0)^( pi)cos2x*log(sin x)dx

If int_(0)^( pi)e^(sin x)dx=p. Then value of int_(0)^((pi)/(2))x cos xe^(sin x)dx is (A) (pi)/(2)e-p(B)(pi)/(2)e-2p (C) (pi)/(2)e-(p)/(2)(D)p

If I_(1)=int_(0)^( pi)x sin xe^(cos4x)dx , and I_(2)=int_(0)^( pi/2)cos xe^(cos4x)dx ,then the value of [(I_(1))/(I_(2))] is (where [.] denotes the greatest integer function)

int_(0)^( pi/2)(sin x)/(1+cos x)dx

"int_(0)^( pi/2)(|sin x|+|cos x|)dx

int_(0)^( pi/2)sin^(2)x cos x dx

int_(0)^(pi//2) x sin x cos x dx

int_(0)^(pi//2) x sin x cos x dx

int_(0)^(pi//2) x sin cos x dx=?