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 area under the curve \(y = \log_e(x + e)\) from 0 to infinity is calculated using the integral: \[ A = \int_0^\infty \log_e(x + e) \, dx \] We can evaluate this integral using integration by parts or by using known results. Using standard integration techniques or tables, the area is found to be: \[ A = 2 \] Thus, the correct answer is \(2\).