Question

Evaluate \( \int_{-4}^{4} \log \left( \frac{8 - x}{8 + x} \right) dx \)

• A. \( -4 \)
• B. 8
• C. 4
• D. 0

Hint:

For symmetric intervals, integrals of even functions are often zero due to symmetry.

Answer 1

The Correct Option is D

Step 1: Simplify the integral.
The given integral is of the form: \[ \int_{-4}^{4} \log \left( \frac{8 - x}{8 + x} \right) dx \] This is an even function, and the integral of an even function over a symmetric interval results in 0.
Step 2: Conclusion.
The value of the integral is \( 0 \).