Question

The area bounded by the curves \( y = \cos x \) and \( y = \sin x \) between the ordinates \( x = 0 \) and \( x = \frac{3\pi}{2} \) is

• A. \( 4\sqrt{2} - 1 \)
• B. \( 4\sqrt{2} + 1 \)
• C. \( 4\sqrt{2} - 2 \)
• D. \( 4\sqrt{2} + 2 \)

Hint:

For areas between curves, always find the points of intersection and integrate the absolute difference of the functions.

Answer 1

The Correct Option is C

To find the area bounded by the curves, we compute the integral of \( \left| \cos x - \sin x \right| \) from \( x = 0 \) to \( x = \frac{3\pi}{2} \).
The result of the integration gives the area \( 4\sqrt{2} - 2 \).