The area enclosed by the curve y = log_e(x + e^ 2 ), x = log_e(2/y) and x = log_e 2, above the line y = 1 is

JEE Main 2022 Mathematics question

The area enclosed by the curve y = + ), x = /y) and x = 2, above the line y = 1 is

(1)2 + e − 2
(2)1 + e − 2Correct
(3)e − 2
(4)1 + 2

Answer: (2)

Solution

The curve x = ln(2/y) is the curve . The required region is the one bounded by , , x = ln 2 and above y = 1 (the printed NTA region). Integrating with respect to y between y = 1 and y = 2: $A =

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Question ID VK-034695