Question

The area intercepted by the curves \( y = \cos x \), \( x \in [0, \pi] \) and \( y = \cos 2x \), \( x \in [0, \pi] \), is

• A. \( \frac{3\pi}{2} \)
• B. \( \frac{3\sqrt{3}}{2} \)
• C. \( \frac{3\pi}{4} \)
• D. \( \frac{3\sqrt{3}}{4} \)

Hint:

To find the area between two curves, subtract the integrals of the two functions over the given interval.

Answer 1

The Correct Option is D

Step 1: Set up the area integral.
To find the area between the curves, set up the definite integrals for both curves and subtract the values. Use the limits from \( 0 \) to \( \pi \).
Step 2: Calculate the area.
After solving the integrals, the area is found to be \( \frac{3\sqrt{3}}{4} \). Final Answer: \[ \boxed{\frac{3\sqrt{3}}{4}} \]