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 or reference integral tables for logarithmic functions to calculate the area under such curves.

Answer 1

The Correct Option is B

The definite integral \(\int_0^\infty \log_e(x + e) \, dx\) represents the area under the curve \(y = \log_e(x + e)\) from 0 to infinity. Evaluating this integral, either through integration by parts or by referencing established integration results, yields an area of \(A = 2\). Therefore, the computed area is \(2\).