FRQ — Integration and Accumulation of Change

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

For each integral, choose an efficient antidifferentiation technique and evaluate exactly.

Total: 8 points

(a) Evaluate $\int \frac{4x}{x^2+9}\,dx$ . State the technique. (2 points)

(b) Evaluate $\int\frac{x^2+2x+5}{x+1}\,dx$ . State the technique. (2 points)

(d) Evaluate $\int_0^4\left(\sqrt{x}+\frac1{x+1}\right)\,dx$ . State the technique. (2 points)

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

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