Evaluate the following definite Integral: ∫(sin^2 x/2 - cos^2 x/2)dx, x ∈ [0, π]

Question

Evaluate the following definite Integral:

\(\int\limits_0^\pi \)\(\Big(\)sin²\(\cfrac{\text x}2-cos^2\cfrac{\text x}2\Big)d\text x\)

Answer 1

Because we have a formula

cos x = cos²\(\cfrac{\text x}2\) - sin²\(\cfrac{\text x}2\)

Remember that ∫sin x = - cos x and ∫cos x = sin x