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The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 is
- 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 x = 0 to x = 3π/2 is calculated by integrating the difference of the two functions over the specified interval, taking into account where each function is greater. The correct option, 4√2 − 2, results from evaluating this integral, which accounts for the intersections and the areas above and below the x-axis.
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