The region of integration is a hemisphere along the positive x axis intersected by the y-z plane
In spherical co-ordinates the region is given by:
By u substitution let u = cosφ so then du = -sinφ dφ and when φ = π, u = -1 and when φ = 0, u = 1
By half angle formula..
By u substitution let u = 2θ so then 1/2du = dθ and when θ = π/2, u = π and when θ = -π/2, u = -π