Integration by Parts

Grade 12 Maths Higher — Integration by Parts: 25 practice questions with instant scoring and explanations.

1. Integration by parts formula: ∫u dv =
2. The choice of u in integration by parts is guided by:
3. LIATE stands for (in order of priority for u):
4. For ∫x·e^x dx, we choose u =
5. ∫x·e^x dx =
6. For ∫x·sin(x)dx, we choose u =
7. ∫x·sin(x)dx =
8. For ∫ln(x)dx, we choose u =
9. ∫ln(x)dx =
10. For ∫x²·e^x dx, using integration by parts twice:
11. ∫e^x·sin(x)dx requires:
12. The special method for ∫e^(ax)sin(bx)dx uses:
13. For ∫x²·cos(x)dx, the pattern suggests:
14. ∫sin⁻¹(x)dx using parts (u = sin⁻¹(x), dv = dx):
15. For ∫sec³(x)dx, reduction formula method uses:
16. ∫sec³(x)dx =
17. Reduction formula for ∫sin^n(x)dx relates to:
18. For ∫x^n·e^x dx, applying parts repeatedly gives formula for:
19. ∫x^n·e^x dx = e^x(x^n - nx^(n-1) + n(n-1)x^(n-2) - ... + C) shows:
20. When applying integration by parts, if result has ∫u dv on both sides:
21. ∫e^x·cos(x)dx: If I = ∫e^x·cos(x)dx using parts cyclically gives:
22. Solving for I when ∫e^(ax)sin(bx)dx = I leads to:
23. Tabular integration by parts applies to:
24. For ∫P(x)·e^(ax)dx where P(x) is polynomial:
25. Review question for Integration by Parts