AP Calculus AB: Fundamental Theorem of Calculus Part 2 and Properties — Drill 1

About This Drill

AP Calculus AB: Fundamental Theorem of Calculus Part 2 and Properties — Drill 1 is a Math practice drill covering FTC Part 2 and Properties. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice evaluating definite integrals using the Fundamental Theorem of Calculus Part 2 and applying properties such as linearity, reversal of limits, and interval additivity. These topics appear on every AP Calculus AB exam.

Questions in This Drill

1. What is the value of \( \int_0^3 (x^2 + 2)\,dx \)?
2. If \( \int_2^7 f(x)\,dx = 10 \), what is the value of \( \int_7^2 f(x)\,dx \)?
3. Suppose \( \int_1^5 f(x)\,dx = 14 \) and \( \int_1^3 f(x)\,dx = 6 \). What is the value of \( \int_3^5 f(x)\,dx \)?
4. If \( \int_0^4 f(x)\,dx = 10 \) and \( \int_0^4 g(x)\,dx = -3 \), what is the value of \( \int_0^4 [3f(x) - 2g(x)]\,dx \)?
5. The function \( f(x) = x^2 - 4 \) is defined on \( [-3, 3] \). Which of the following correctly describes the relationship between \( \int_{-3}^{3} f(x)\,dx \) and \( \int_{-3}^{3} |f(x)|\,dx \)?