Evaluate the following definite integral: `int_0^pi(sin^2x/2-cos^2x/2)dx`

Explanation

Take `I=int_{0}^{pi}(sin ^{2} frac{x}{2}-cos ^{2} frac{x}{2}) d x `
`
=-int_{0}^{pi}(cos ^{2} frac{x}{2}-sin ^{2} frac{x}{2}) d x `
`
=-int_{0}^{pi} cos x d x `
`
Rightarrow int cos x d x=sin x=F(x) `


According to the second fundamental theorem of calculus, we get


`I=F(pi)-F(0) `
`
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