Integration using Partial Fractions
Maths Higher · Grade 12 · Week 21 · 25 questions
This Grade 12 mathematics chapter on Integration using Partial Fractions is high-yield for CBSE + JEE, exploring core concepts. For JEE, speed on these standard problem types is critical — build fluency through timed practice.
What you'll practise
- Master the key derivations and worked examples from NCERT for integration using partial fractions
- Solve CBSE board-pattern problems from integration using partial fractions including NCERT exemplar-level questions
All 25 questions in this Integration using Partial Fractions quiz
Grade 12 Maths Higher — Integration using Partial Fractions: 25 practice questions with instant scoring and explanations.
- Partial fraction decomposition applies to:
- For rational function P(x)/Q(x) where deg(P) ≥ deg(Q):
- For 1/(x-a), the partial fraction is:
- For 1/((x-a)(x-b)) where a ≠ b, decompose as:
- For 1/(x²(x-1)), the decomposition is:
- For 1/((x-a)^n), the partial fraction includes:
- ∫1/((x-1)(x-2))dx using partial fractions:
- For 1/((x-1)(x+1)), A and B in A/(x-1) + B/(x+1) are:
- For quadratic factor (ax² + bx + c) in denominator (irreducible):
- ∫(2x+1)/(x²+1)dx can be split as:
- For ∫1/(x(x²+1))dx, decompose as:
- After finding A, B, C... in partial fractions, integrate each term by:
- For ∫x/(x²-1)dx, partial fractions give:
- Using cover-up method for A/(x-a) in decomposition:
- ∫(x+2)/(x²-3x+2)dx using partial fractions:
- For improper fractions (deg P ≥ deg Q):
- ∫1/(x³+1)dx requires factoring x³+1 as:
- For complex roots in denominator, partial fractions still work:
- ∫dx/(x(1+x)) equals:
- Partial fraction decomposition assumes denominator is:
- For ∫P(x)/Q(x)dx where deg(P) < deg(Q), we can:
- The advantage of partial fractions over other methods is:
- For repeated linear factors (x-a)^n in Q(x):
- ∫(3x+5)/(x²+5x+6)dx after partial fractions and integration gives:
- ∫ 1/(x²-1) dx equals:
Question 1 of 250 correct so far