Integration by Parts
Maths · Grade 12 · Week 21 · 25 questions
This quiz focuses on Integration by Parts — an important area in Grade 12 mathematics. A strong foundation in integration by parts is critical for board exam success and prepares you for undergraduate mathematics and data science.
What you'll practise
- Apply key formulas and equations for integration by parts
- Understand core concepts of integration by parts
- Test your knowledge of integration by parts through varied questions
- Build confidence with integration by parts through practice
All 25 questions in this Integration by Parts quiz
Grade 12 Maths — Integration by Parts: 25 practice questions with instant scoring and explanations.
- The integration by parts formula is:
- For ∫ x sin(x) dx, a good choice is:
- ∫ x sin(x) dx using parts (u = x, dv = sin(x)dx) equals:
- For ∫ x eˣ dx, the best choice is:
- ∫ x eˣ dx using parts equals:
- For ∫ x cos(x) dx, the best choice is:
- ∫ x cos(x) dx equals:
- For ∫ ln(x) dx, a good choice is:
- ∫ ln(x) dx equals:
- For ∫ x² eˣ dx, the first parts gives u dv where:
- ∫ x² eˣ dx requires integration by parts:
- For ∫ eˣ sin(x) dx, the appropriate strategy is:
- For ∫ x² cos(x) dx, the best first choice is:
- ∫ x² cos(x) dx gives (after simplification):
- The LIATE rule for choosing u prioritizes:
- For ∫ x tan⁻¹(x) dx, the LIATE rule suggests u = :
- ∫ e^x cos(x) dx can be solved by:
- For ∫ x√(1 + x) dx, the best approach is:
- ∫ x³ sin(x) dx requires parts:
- For ∫ (ln(x))² dx, the first choice is u = :
- The product ∫ xe^(2x) dx can be solved by parts with u, dv as:
- ∫ xe^(2x) dx equals:
- When using integration by parts, the key is to choose u and dv such that:
- ∫ x·eˣ dx:
- ∫ x·ln x dx:
Question 1 of 250 correct so far