The area enclosed by the curves y = log e x + e 2 , x = log e 2 y and x = log e 2 , above the line y = 1 is

Step-by-step solution

The area enclosed by the curves y = log e x + e 2 ,   x = log e 2 y and x = log e 2 , above the line y = 1 is Now plotting the diagram of given functions we get, According to JEE Mains, we have to calculate the required region A 2 which is shaded in crossed lines and comes out to be A 2 = ∫ 1 2 ln 2 y - e y + e 2 d y = 1 + e - ln 2 But according to the question the required region A 1 comes out to be shaded in parallel lines, which can be obtained as A 1 = ∫ 0 ln 2 ln x + e 2 - 2 e - x d x = x + e