AP Calculus AB: Fundamental Theorem of Calculus Part 1 — Drill 1

About This Drill

AP Calculus AB: Fundamental Theorem of Calculus Part 1 — Drill 1 is a Math practice drill covering Fundamental Theorem of Calculus. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice applying the Fundamental Theorem of Calculus Part 1 to differentiate accumulation functions, including cases where the chain rule is required. These AP Calculus AB skills are central to both the multiple-choice and free-response sections.

Questions in This Drill

1. If \( F(x) = \displaystyle\int_3^x (t^2+1)\,dt \), then \( F'(x) = \)
2. If \( G(x) = \displaystyle\int_0^{x^3} \sin(t)\,dt \), then \( G'(x) = \)
3. If \( H(x) = \displaystyle\int_x^{5} e^{t^2}\,dt \), then \( H'(x) = \)
4. Let \( A(x) = \displaystyle\int_0^x f(t)\,dt \), where \( f \) is continuous, \( f(t) > 0 \) on \( (0,2) \), \( f(2) = 0 \), and \( f(t) < 0 \) on \( (2,5) \). Which of the following must be true?
5. Let \( P(x) = \displaystyle\int_{x^2}^{7} \sqrt{1+t^3}\,dt \). Which of the following equals \( P'(x) \)?