Question

The area bounded by the curve y = log_e x and x-axis and the straight line x = e is

A. e sq. units

B. 1 sq. units

C. \(1-\frac{1}{e}\) sq. units

D. \(1+\frac{1}{e}\) sq. units

Answer 1

Correct answer is B.

We need to find the area of the blue shaded region.

At, x = 1, y = log_e (1) = 0

And, at x = e, y = log_e (e) = 1

These are our bounds.

So, this will be computed as –

Using Integration by parts,