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Find the area enclosed by the graphs of y = cos x and y = sin x for x ranging from 0 to 3π/2.
- 4√2 + 2
- 4√2 − 1
- 4√2 + 1
- 4√2 − 2
Correct answer: 4√2 − 2
Solution
The area between the curves y = cos x and y = sin x from 0 to 3π/2 is calculated by integrating the difference of the two functions over the specified interval. The correct option, 4√2 − 2, results from evaluating this integral and accounting for the points where the curves intersect.
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