What is \( \int_0^4 \frac{f(x)}{g(x)} dx \) equal to ?
For the next two (02) items that follow : Let \( f(x) = \sin x \) and \( g(x) - f(x) = f(4 - x) \).
- A. 0
- B. 1
- C. 2 ✓
- D. 4
Correct Answer: C. 2
Explanation
Given \( g(x) = f(x) + f(4-x) \). Let the integral be I. Using King's rule \( \int_0^a h(x) dx = \int_0^a h(a-x) dx \), we have \( I = \int_0^4 \frac{f(4-x)}{f(4-x) + f(x)} dx \). Adding both expressions for I gives \( 2I = \int_0^4 1 dx = 4 \), so I = 2.
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