Calculus BC · Unit 8 · Paper 1

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 1 Paper 2 Paper 3

Each paper is built from this unit’s 24 terms and is the same for everyone, so a teacher can assign “Unit 8, Paper 1” 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

Area between two curves

MVT for integrals

Upper curve can switch

Volume by disks and washers

Cross-section area formulas

Net change from a rate in an applied context

Switch variables before splitting

Choosing dx or dy

Arc length comes from Pythagoras

Average value divides by the width

Average value keeps the function's units

Arc length of a parametric curve

Short answer 1. Define or explain: Test which curve is on top

3 pts

Short answer 2. Define or explain: Horizontal slices mean right minus left

3 pts

Short answer 3. Define or explain: Total distance from a velocity function

3 pts

Short answer 4. Define or explain: Vertical slices mean top minus bottom

3 pts

Free response

9 pts

NO CALCULATOR. Answer the following questions about improper integrals and arc length.

A. Determine whether ∫₁^∞ x^(−3/2) dx converges or diverges. If it converges, find its value.

B. Determine whether ∫₀¹ x^(−1/2) dx converges or diverges. If it converges, find its value.

C. Find the length of the curve y = (2/3)x^(3/2) from x = 0 to x = 3.

D. Determine whether ∫₁^∞ (1/x) dx converges or diverges. Justify your answer, and explain how the result compares with part A.