Question

The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:

• A. 2
• B. 3
• C. 0
• D. 5

Hint:

Remember that the integral of any odd function over a symmetric interval about zero is always zero.

Answer 1

The Correct Option is C

We are given the integral: \[ \int_{\pi/2}^{-\pi/2} \sin x \, dx \] Step 1: Evaluate the integral Since \( \sin x \) is an odd function and the limits of integration are symmetric around zero, we know that the integral of an odd function over a symmetric interval is zero: \[ \int_{-\pi/2}^{\pi/2} \sin x \, dx = 0 \] Thus, the correct answer is \( 0 \).