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Evaluate : int(-pi/2) ^(pi/2) sin^2x dx...

Evaluate : `int_(-pi/2) ^(pi/2) sin^2x dx`

Text Solution

Verified by Experts

`" Let "I= f(x) =sin^(2) x `
`rArr " "f(-x) =[sin(-x)]^(2)=(-sinx)^(2)`
`rArr f(x)` is an even function
` :. int _(-pi//2)^(pi//2) sin^(2) x dx =2int_(0)^(pi//2) sin^(2) x dx`
`=2int_(0)^(pi//2) (1-cos 2x)/(2)dx`
`=int_(0)^(pi//2)(1-cos 2x) dx`
`=[x-(sin 2x)/(2)]_(0)^(pi//2)`
`=((pi)/(2)-(1)/(2)sinpi )-(0-0)=(pi)/(2)`
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