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int(0)^( pi/2) (cos x-sin x)^(2)dx...

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

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

int_(0)^(pi//2)(cos x)/(4-sin^(2)x)dx =

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

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

The value of int_(0)^(2 pi)|cos x-sin x|dx is

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

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