AP Calculus AB 6.8 Finding Antiderivatives and Indefinite Integrals - MCQs - Exam Style Questions
No-Calc Question
\(\ \displaystyle \int \frac{x^{2}}{4}\,dx=\)
(A) \( \dfrac{x}{2}+C\)
(B) \( \dfrac{x^{3}}{12}+C\)
(C) \( \dfrac{x^{3}}{4}+C\)
(D) \( \dfrac{3x^{3}}{4}+C\)
(B) \( \dfrac{x^{3}}{12}+C\)
(C) \( \dfrac{x^{3}}{4}+C\)
(D) \( \dfrac{3x^{3}}{4}+C\)
▶️ Answer/Explanation
Pull out \(\frac{1}{4}\).
\(\displaystyle \int \frac{x^{2}}{4}\,dx=\frac{1}{4}\int x^{2}\,dx\).
\(\displaystyle =\frac{1}{4}\cdot \frac{x^{3}}{3}+C=\frac{x^{3}}{12}+C\).
✅ Answer: (B)