Question

The integral $ \int_0^1 \frac{1}{2 + \sqrt{2e}} \, dx $ is:

• A. \( \frac{1}{2} \ln (2 + \sqrt{2e}) \)
• B. \( \frac{1}{\sqrt{2}} \)
• C. \( \frac{1}{\sqrt{2}} \ln (2 + \sqrt{2e}) \)
• D. \( \frac{1}{2 \sqrt{2}} \)

Hint:

For integrals involving constants, the solution is often as simple as multiplying the constant by the length of the integration interval.

Answer 1

The Correct Option is D

The given integral is: \[ \int_0^1 \frac{1}{2 + \sqrt{2e}} \, dae \] 
Since this is a straightforward integral with respect to \( a \), we can directly integrate the expression. The integration is relatively simple as the denominator is constant with respect to \( a \), so the result of the integral is: \[ \frac{1}{2\sqrt{2}} \] 
Thus, the correct answer is \( \frac{1}{2 \sqrt{2}} \).