AP Calculus AB Unit 6.7: Fundamental Theorem
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
6.7 The Fundamental Theorem of Calculus and Definite Integrals 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≤12, selected values of C(t) are given in the table shown.
For 12≤t≤20, the rate of change of the temperature of the coffee is modeled by C′(t)=t−24.55e0.01t, where C′(t) is measured in degrees Celsius per minute. Find the temperature of the coffee at time t=20. Show the setup for your calculations.
(c)
12
20,
t
0.01
24.55,
t
e
C t
t
C t
20.
t
20
12
20
12
C
C
C t dt
Integral
1 point
Uses initial condition
1 point
55
14.670812
40.329188
The temperature of the coffee at time
20
t
is 40.329 degrees
Celsius.
Answer
1 point
AP® Calculus AB/BC 2024 Scoring Guidelines
Scoring notes:
.
C t
20
12
20
55
14.670812
C
C t dt
20
12
14.670812
40.329188
C t dt
dt
o
20
12
20
12
C
C
C t
20
12
20
55
C
C t
o
20
12
20
12
C
C t
C
20
12
20
55
C
C t
12
C
55
12,
55
14.671
14.671
55
40.329
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