Question

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is ______.

Options

• 3 sq. units

• 4 sq. units

• 1 sq. unit

• 2 sq. units

Answer 1

The area enclosed between the curve y = log_e(x + e) and the coordinate axes is 1 sq. unit.

Explanation:

Required area = `int_{1-e}^0log_e(x + e)dx`

= `int_1^e log_e t dt` ....[Put (x + e) = t and dx = dt]

= `[t log_e t - t]_1^e`

= 1 sq. unit