Question

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

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Use integration by parts to calculate the area under logarithmic curves.

Answer 1

The Correct Option is B

The area under the curve is given by: \[ A = \int_0^\infty \log_e(x + e) \, dx \] Evaluating this integral using integration by parts or known results yields: \[ A = 2 \] Consequently, the enclosed area is \(2\).