Find the area between y = sin x and y = cos x from x = 0 to x = π/2.

Question

G1 Physics · Accepted Answer

The curves intersect where sinx=cosx, i.e. x=π/4. Area = ∫₀→π/4(cosx−sinx)dx + ∫π/4→π/2(sinx−cosx)dx. Each part equals √2−1. Total area = 2(√2−1).