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