Question

Evaluate the integral \[ \int_{-5}^{5} \log \left( \frac{7 - x}{7 + x} \right) \, dx \]

• A. 5
• B. 0
• C. -5
• D. 10

Hint:

For integrals of odd functions over symmetric intervals, the result is always 0.

Answer 1

The Correct Option is B

Step 1: Analyze the symmetry of the function.
The given function \( \log \left( \frac{7 - x}{7 + x} \right) \) is an odd function because replacing \( x \) with \( -x \) results in the negative of the original function. The integral of an odd function over a symmetric interval \( [-a, a] \) is 0.

Step 2: Conclusion.
Thus, the value of the integral is 0, corresponding to option (B).