Question

If \( f(x) = \cos x + 1 \) and \( f'(x) = 2 \cos x \), then \[ \int_0^\frac{\pi}{2} f(x)dx \] is equal to

• A. \( \frac{1}{3} \)
• B. \( \frac{5}{3} \)
• C. \( \frac{1}{2} \)
• D. 1

Hint:

To evaluate definite integrals, integrate the function over the limits and substitute the values.

Answer 1

The Correct Option is D

Step 1: Integrate the function.
Using the given function \( f(x) = \cos x + 1 \), we can integrate it from 0 to \( \frac{\pi}{2} \).
Step 2: Conclusion.
Thus, the integral of \( f(x) \) over the given interval is 1.
Final Answer: \[ \boxed{1} \]