What is \int_{0}^{8\pi}|\sin x|dx equal to?
- A. 2
- B. 4
- C. 8
- D. 16 ✓
Correct Answer: D. 16
Explanation
The function |\sin x| is periodic with a period of \pi. Therefore, the integral from 0 to 8\pi is 8 times the integral from 0 to \pi. The integral \int_0^\pi \sin x \, dx = [-\cos x]_0^\pi = -(-1) - (-1) = 2. Multiplying by 8, we get 8 \times 2 = 16.
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