Integration by Parts
Maths Higher · Grade 12 · Week 22 · 25 questions
This Grade 12 mathematics chapter on Integration by Parts is high-yield for CBSE + JEE, exploring core concepts. Board paper almost always contains one 5-mark proof and two 3-mark application problems from this area.
What you'll practise
- Master the key derivations and worked examples from NCERT for integration by parts
- Solve CBSE board-pattern problems from integration by parts including NCERT exemplar-level questions
All 25 questions in this Integration by Parts quiz
Grade 12 Maths Higher — Integration by Parts: 25 practice questions with instant scoring and explanations.
- Integration by parts formula: ∫u dv =
- The choice of u in integration by parts is guided by:
- LIATE stands for (in order of priority for u):
- For ∫x·e^x dx, we choose u =
- Using the standard identity, the value of ∫x·e^x dx is:
- For ∫x·sin(x)dx, we choose u =
- Using the standard identity, the value of ∫x·sin(x)dx is:
- For ∫ln(x)dx, we choose u =
- Using the standard identity, the value of ∫ln(x)dx is:
- For ∫x²·e^x dx, using integration by parts twice:
- ∫e^x·sin(x)dx requires:
- The special method for ∫e^(ax)sin(bx)dx uses:
- For ∫x²·cos(x)dx, the pattern suggests:
- ∫sin⁻¹(x)dx using parts (u = sin⁻¹(x), dv = dx):
- For ∫sec³(x)dx, reduction formula method uses:
- Using the standard identity, the value of ∫sec³(x)dx is:
- Reduction formula for ∫sin^n(x)dx relates to:
- For ∫x^n·e^x dx, applying parts repeatedly gives formula for:
- ∫x^n·e^x dx = e^x(x^n - nx^(n-1) + n(n-1)x^(n-2) - ... + C) shows:
- When applying integration by parts, if result has ∫u dv on both sides:
- ∫e^x·cos(x)dx: If I = ∫e^x·cos(x)dx using parts cyclically gives:
- Solving for I when ∫e^(ax)sin(bx)dx = I leads to:
- Tabular integration by parts applies to:
- For ∫P(x)·e^(ax)dx where P(x) is polynomial:
- ∫ x·eˣ dx equals:
Question 1 of 250 correct so far