IB Integration Challenge Worksheet

Name:

Date:

📊 Part 1: Advanced Integration Techniques

1. Evaluate ∫ x²e^(3x) dx using integration by parts.

2. Find ∫ (2x + 1)/(x² + x - 6) dx using partial fractions.

3. Calculate ∫₀^(π/2) sin³x cos²x dx

4. Evaluate ∫ √(4 - x²) dx using trigonometric substitution.

🎯 Part 2: Application Problems

5. A particle moves along a line with velocity v(t) = te^(-t²) m/s. Find the displacement from t = 0 to t = 2 seconds.

6. The region bounded by y = ln(x), x = e, and y = 0 is rotated about the y-axis. Find the volume of the solid formed.

7. Find the area between the curves y = x sin(x) and y = 0 from x = 0 to x = π.

⭐ Part 3: Challenge Extensions

8. Advanced: Prove that ∫₀^∞ e^(-x²) dx = √π/2 by using the substitution u = x√2 and properties of the gamma function.

9. Investigation: For what values of n does ∫₁^∞ 1/x^n dx converge? Explain your reasoning and show all calculations.

Success Criteria:

✓ Apply integration by parts correctly
✓ Use partial fractions for rational functions
✓ Solve real-world applications involving integration
✓ Demonstrate understanding of convergence/divergence

Differentiation Support: Use formula sheets as needed. Start with questions 1, 3, 5 for core understanding before attempting extensions.

IB Integration Challenge Worksheet

IB Integration Challenge Worksheet

📊 Part 1: Advanced Integration Techniques

🎯 Part 2: Application Problems

⭐ Part 3: Challenge Extensions

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

More Mathematics Worksheets

Year 9 Financial Mathematics

Year 9 Financial Mathematics

Mathematics and Statistics Practice

Explore more free resources