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

Answer»

Solution :`int_(0)^(pi//2)COS^(2)x DX =int_(0)^(pi//2)((cos2x +1)/(2))dx`
`=(1)/(2) int_(0)^(pi//2)cos 2x dx +(1)/(2)int_(0)^(pi//2)1DX`
`=(1)/(2)[(sin 2x)/(2)]_(0)^(pi//2)+(1)/(2)[x]_(0)^(pi//2)`
`=(1)/(2)[((sinpi)/(2)-(sin 0)/(2))+((pi)/(2)-0)]=(pi)/(4)`


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