Evaluate: ∫ (a cos^2x+b sin^2x)dx, x ∈[0, π/2]

Question

Evaluate:  

\(\int\limits_0^{\pi/2}(a\,cos^2x+b\,sin^2x)dx\)

∫ (a cos²x+b sin²x)dx, x ∈[0, π/2]

Answer 1

\(=\cfrac{\pi}{4}(a+b)\)