The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area A . Then A 4 is equal to

Step-by-step solution

A = ∫ π / 4 5 π / 4 sin x - cos x d x = - cos x - sin x π / 4 5 π / 4 = - - 1 2 - - 1 2 - - 1 2 - 1 2 ⇒   A = 2 2 + 2 2 = 2 2 sq. units ⇒   A 4 = 2 2 4 = 16 × 4 = 64