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

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

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`"Let I "= int_(0)^(pi//2) cos^(2) x dx`
`rArr I= int_(0)^(pi//2)cos^(2) ((pi)/(2)-x)dx`
`( :' int_(0)^(a) f(x) dx= int_(0)^(a) f(a-x)dx)`
`I = int_(0)^(pi//2) sin^(2) xdx`
Adding equations (1) and (2)
`2I =int_(0)^(pi//2) (sin^(2)x+cos^(2)x) dx`
`=int_(0)^(pi//2)1 dx " "( :' sin^(2) x+cos^(2) x=1)`
`=[x]_(0)^(pi//2) =(pi)/(2)-0 rArr I=(pi)/(4)`
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