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int(0)^(3/2)|x*cos pi x|dx...

int_(0)^(3/2)|x*cos pi x|dx

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If I_(1)=int_(0)^(pi//2)"x.sin x dx" and I_(2)=int_(0)^(pi//2)"x.cos x dx" , then

int_(0)^(pi//2) cos 3x dx

int_(0)^(pi//2) cos 3x dx

int_(0)^(2 pi)|cos x|dx

If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

If I_(1)=int_(0)^(pi//2) cos(sin x) dx,I_(2)=int_(0)^(pi//2) sin (cos x) dx and I_(3)=int_(0)^(pi//2) cos x dx then

int_(0)^( pi)|cos x|^(3)dx

Show that: int _(0) ^((3)/(2)) | x cos \pi x | dx = ( 5 pi -2)/(2 pi ^(2))