The area of the region bounded by the lines x = 1 ,   x = 2 , and the curves x y - e x = sin x and 2 x y = 2 sin x + x 3 is

Step-by-step solution

The area of region bounded by the curves x y - e x = sin x or y = sin x x + e x and 2 x y = 2 sin x + x 3 or y = sin x x + x 2 2 between lines x = 1 and x = 2 is A = ∫ 1 2 sin x x + e x - sin x x + x 2 2 d x = ∫ 1 2 e x - x 2 2 d x = e x - x 3 6 1 2 = e 2 - e - 7 6