What is the area between the curve y = sinx and the x-axis in the interval \( \left[\frac{\pi}{4}, \frac{\pi}{2}\right] \) ?
For the next two (02) items that follow : Let k be the area between the curve y = sinx and x-axis in the interval \( \left[0, \frac{\pi}{4}\right] \)
- A. k
- B. 1 - k ✓
- C. \frac{\pi-k}{2}
- D. \frac{\pi-2k}{2}
Correct Answer: B. 1 - k
Explanation
The total area under \( y = \sin x \) from 0 to \( \frac{\pi}{2} \) is 1. If the area from 0 to \( \frac{\pi}{4} \) is k, then the area from \( \frac{\pi}{4} \) to \( \frac{\pi}{2} \) is strictly 1 - k.
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