Unit 8: Applications of Integration
Calculus AB · Unit 8 · Paper 2

Applications of Integration unit test

A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.

Paper 1Paper 2Paper 3
Each paper is built from this unit’s 39 terms and is the same for everyone, so a teacher can assign “Unit 8, Paper 2” and every student sits the identical test. Multiple choice is marked objectively; the written sections you mark yourself against the model answer and rubric.
Suggested time 36 min 33 points0/17 attempted
1

Square cross section

2

Horizontal slices mean right minus left

3

Average value versus average rate of change

4

Washer inner and outer radii

5

Equilateral triangle cross section

6

Area between two curves

7

Volume of revolution about a horizontal line

8

Interpreting average value

9

MVT for integrals

10

Choosing disks or washers

11

Area is never negative

12

Integrating with respect to y

Short answer 1. Define or explain: Mean Value Theorem for integrals

3 pts

Short answer 2. Define or explain: Volume by disks

3 pts

Short answer 3. Define or explain: Semicircle on diameter s

3 pts

Short answer 4. Define or explain: Limits come from intersections

3 pts

Free response

9 pts

A particle moves along the x-axis with velocity v(t) = t² − 4t + 3 meters per second for 0 ≤ t ≤ 4 seconds. At time t = 0 the particle is at position x = 2 meters.

Find all times in the interval at which the particle is at rest, and find the intervals on which it is moving to the right.

Find the position of the particle at time t = 4.

Find the total distance traveled by the particle over the interval [0, 4].