Finding value of p for area of region

Question

The region bounded by the x-axis and y = sinx between x = 0 and x = π is separated into two regions

by the line x = p . If the area of the region for 0 ≤ x≤ p exceeds the area of the region for p ≤ x ≤ π by

one square unit, then p =

Answer 1

A₁ = ∫₀^psinxdx = - cosx₀^p = 1 - cosp;

A₂ = ∫_p^πsinxdx = - cosx_p^π = 1 + cosp;

A₁ = A₂ + 1; 1 - cosp = 1 + cosp + 1; 2cosp = -1; cosp = -1/2

p = 2π/3