Integration Rapid Review for AP Calculus

Review the following concepts if needed:

• Evaluating Basic Integrals for AP Calculus
• Integration by U-Substitution for AP Calculus
• Techniques of Integration for AP Calculus

Review Problems and Answers

1. Evaluate .

Answer: Rewrite as .

2. Evaluate

Answer: Rewrite as .

3. Evaluate

Answer: Rewrite as . Let u = x ² – 1.

Thus, .

4. Evaluate .

Answer: –cos x + C.

5. Evaluate

Answer: Let u =2x and obtain .

6. Evaluate

Answer: Let u = ln x; and obtain .

7. Evaluate

Answer:Let u = x²; and obtain .

8. Evaluate

Answer: Let u = x, du = dx, dv = cos xdx, and v = sin x,

then .

9. Evaluate

Answer: .