Question

If ∫dx/(√(1 + x) + √(1 – x) + 2) for x ∈ [0,1] = a√2 – (π/2) + c where a, b, c ∈ N, find the value of (a + b + c).

Answer 1

We have,

Put x = sin(2θ) 

dx = 2cos(2θ) dθ 

Thus, a = 2, b = 2, c = – 1 

Hence, the value of (a + b + c) = 3.