Question

Let $f(x) = \int_{1}^{x} \sin^2 \left(\frac{t}{2}\right) dt$. Then the value of $\lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x}$ is equal to:

• A. \( \frac{1}{4} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{3}{4} \)
• D. \( 1 \)
• E. \( 0 \)

Hint:

Don't waste time actually integrating the function! Most calculus problems involving a limit of an integral are testing your knowledge of the Fundamental Theorem of Calculus.

Answer 1

The Correct Option is D