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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

Evaluate ∫02xx2+5 dx\int_0^2 x\sqrt{x^2+5}\,dx exactly.
Total: 5 points

(a) Identify a change of variable that simplifies the radical, and transform the bounds. (2 points)

(b) Rewrite the integral entirely in terms of the new variable. (1 point)

(c) Evaluate the integral exactly. (2 points)

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