The area of the region enclosed by the curves y = x , x = e , y = 1/x and the positive x -axis is: - Mathematics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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The area of the region enclosed by the curves y = x, x = e, y = 1/ x and the positive x -axis is:

Solution & Step-by-step Explanation

The curves are y = x and y = 1/ x . They intersect at x = 1 (for x > 0).The region is bounded by the x -axis, y = x (from 0 to 1), and y = 1/ x (from 1 to e).Area = \int_{0}^{1} x d x + \int_{1}^{e} \frac{1}{x} d x $ = [\frac{x ^{2}}{2}]_{0}^{1} + [ln x]_{1}^{e} = \frac{1}{2} + (ln e - ln 1) = \frac{1}{2} + 1 = \frac{3}{2} $

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The area of the region enclosed by the curves y = x, x = e, y = 1/ x and the positive x -axis is:

1 square unit

3/2 square units

5/2 square units

1/2 square unit

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