The area enclosed by the curves y = sin x + cos x and y = cos x - sin x over the interval 0 , π 2 is

Step-by-step solution

The given curves are y = sin x + cos x   &   y = cos x - sin x y 1 = sin x + cos x = 2  sin x + π 4 y 2 = 2 | sin π 4 - x | So, Required Area = ∫ 0 π 4 sin x + cos x - cos x - sin x dx + ∫ π 4 π 2 sin x + cos x - sin x - cos x dx 2 ∫ 0 π 4 sin x d x + 2 ∫ π 4 π 2 cos x d x = 4 - 2 2 = 2 2 2 - 1 .