FRQ — Applications of Integration

Free response·Challenge (5/5)·No calculatorNeeds mentor review

Difficulty guide

The label describes the problem, not your ability.

1/5 - Foundational

Warm-up setup; checks one basic idea.

2/5 - Routine exam skill

Normal syllabus skill; usually one main rule or interpretation.

3/5 - Standard multi-step

Exam-style problem with multiple steps or a common trap.

4/5 - Hard exam skill

High-end exam problem; combines methods carefully.

5/5 - Challenge

Stretch problem beyond normal exam pressure.

Question

Let

R

be the region between

y=x

and

y=x^2

for

0\le x\le1.

The region is revolved about

y=2.

Total: 6 points

(a) Identify the outer radius and inner radius of a typical washer. (2 points)

(b) Set up an integral for the volume. (2 points)

(d) A student writes $\pi\int_0^1(x-x^2)^2\,dx$ . Explain the student's error. (1 point)

Your response (optional — you can also work on paper)

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