Question

Find the value of ∫(sin^–1 [x² + (1/2)] + cos^–1 [x² – (1/2)]) dx for x ∈ [-1,1], where [,] = GIF. 

Answer 1

Let 

= π(1 – (1/√2)) + π(1 + (1/2√2)) 

= 2π