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" 4.If "I=int(0)^( pi/2)(n(sin x)dx" the...

" 4.If "I=int_(0)^( pi/2)(n(sin x)dx" then "int_(-pi/4)^( pi4)ln(sin x+cos x)dx

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If I_(1) = int_(0)^(pi//2)ln (sin x)dx , I_(2)=int_(-pi//4)^(pi//4)ln (sin x + cos x)dx , then :

Evaluate: int_(-pi/4)^( pi/4)log(sin x+cos x)dx

int_(0)^( pi/4)(sin x-cos x)dx

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

If int_(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int_(0)^(pi) ln (1+ cos x) dx=

int_(0)^(pi)sin 5 x cos 4x dx=

int_(0)^(pi) sin^(4) x cos^(5) x dx

" (8) "int_(0)^( pi)sin x*cos^(4)x*dx

If int_(0)^(pi//2) sin^(6) x dx = (pi)/(32) then int_(-pi)^(pi) (sin^(6)x + cos^(6) x)dx=