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AP Calculus AB 6.7 The Fundamental Theorem of Calculus and Definite Integrals Questions

Practice AP Calculus Unit 6.7 questions on evaluating definite integrals analytically with antiderivatives and the Fundamental Theorem.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

Exam points

  • evaluate definite integrals by finding an antiderivative and applying the Fundamental Theorem of Calculus

Covered syllabus points

FUN-6.B—Evaluate definite integrals analytically using the Fundamental Theorem of Calculus

Question 1

[Maximum number: 3]

The temperature of coffee in a cup at time t minutes is modeled by a decreasing differentiable function C, where C(t) is measured in degrees Celsius. For 0≤t≤120 \leq t \leq 12, selected values of C(t) are given in the table shown.

For 12≤t≤2012 \leq t \leq 20, the rate of change of the temperature of the coffee is modeled by C′(t)=−24.55e0.01ttC^{\prime}(t)=\frac{-24.55 e^{0.01 t}}{t}, where C′(t)C^{\prime}(t) is measured in degrees Celsius per minute. Find the temperature of the coffee at time t=20. Show the setup for your calculations.

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