Integration using Partial Fractions

Grade 12 Maths Higher — Integration using Partial Fractions: 25 practice questions with instant scoring and explanations.

1. Partial fraction decomposition applies to:
2. For rational function P(x)/Q(x) where deg(P) ≥ deg(Q):
3. For 1/(x-a), the partial fraction is:
4. For 1/((x-a)(x-b)) where a ≠ b, decompose as:
5. For 1/(x²(x-1)), the decomposition is:
6. For 1/((x-a)^n), the partial fraction includes:
7. ∫1/((x-1)(x-2))dx using partial fractions:
8. For 1/((x-1)(x+1)), A and B in A/(x-1) + B/(x+1) are:
9. For quadratic factor (ax² + bx + c) in denominator (irreducible):
10. ∫(2x+1)/(x²+1)dx can be split as:
11. For ∫1/(x(x²+1))dx, decompose as:
12. After finding A, B, C... in partial fractions, integrate each term by:
13. For ∫x/(x²-1)dx, partial fractions give:
14. Using cover-up method for A/(x-a) in decomposition:
15. ∫(x+2)/(x²-3x+2)dx using partial fractions:
16. For improper fractions (deg P ≥ deg Q):
17. ∫1/(x³+1)dx requires factoring x³+1 as:
18. For complex roots in denominator, partial fractions still work:
19. ∫dx/(x(1+x)) equals:
20. Partial fraction decomposition assumes denominator is:
21. For ∫P(x)/Q(x)dx where deg(P) < deg(Q), we can:
22. The advantage of partial fractions over other methods is:
23. For repeated linear factors (x-a)^n in Q(x):
24. ∫(3x+5)/(x²+5x+6)dx after partial fractions and integration gives:
25. Review question for Integration using Partial Fractions