Question

Prove that ∫sin^-1 (√t) dt for t ∈ [0,sin²x] + ∫ cos^–1 (√t) dt for t ∈ [0,cos²x] = π/4  

Answer 1

Let

= (sin^–1 (|sin x|) – cos^–1 (|cos x|)) sin2x 

= (sin^–1 (sin x) – cos^–1 (cos x)) sin 2x = 0 

f'(x) = 0 

f(x) = c

Let