Integration by Substitution
Maths · Grade 12 · Week 20 · 25 questions
This quiz focuses on Integration by Substitution — an important area in Grade 12 mathematics. A strong foundation in integration by substitution is critical for board exam success and prepares you for undergraduate mathematics and data science.
What you'll practise
- Understand core concepts of integration by substitution
- Test your knowledge of integration by substitution through varied questions
- Build confidence with integration by substitution through practice
All 25 questions in this Integration by Substitution quiz
Grade 12 Maths — Integration by Substitution: 25 practice questions with instant scoring and explanations.
- In integration by substitution, if u = g(x), then:
- For ∫ (2x + 1)⁵ dx, the best substitution is:
- For ∫ x·e^(x²) dx, the best substitution is:
- ∫ (3x + 1)⁴ dx using substitution u = 3x + 1 equals:
- ∫ e^(2x) dx using substitution u = 2x equals:
- ∫ sin(3x) dx using substitution u = 3x equals:
- ∫ 1/(2x + 1) dx using substitution u = 2x + 1 equals:
- ∫ cos(5x) dx using substitution u = 5x equals:
- For ∫ x cos(x²) dx, the substitution u = x² gives:
- ∫ (2x)(x² + 1)³ dx using substitution u = x² + 1 gives:
- For ∫ e^(−x) dx, using u = −x gives:
- ∫ 1/√(2x + 1) dx using substitution u = 2x + 1 equals:
- For ∫ x(x² − 1)^(1/2) dx, the best substitution is:
- ∫ (cos(x))sin(x) dx using u = cos(x) gives:
- For ∫ 3e^(3x) dx, the substitution u = 3x gives:
- ∫ x²(x³ + 2)⁴ dx using u = x³ + 2 gives:
- For ∫ sec²(x) dx, is substitution needed?
- ∫ sin(ax + b) dx using u = ax + b gives:
- For ∫ f'(x)/f(x) dx, the result is:
- ∫ (tan(x))sec²(x) dx using u = tan(x) gives:
- For ∫ dx/(ax² + b), if a > 0, b > 0:
- ∫ (1 + ln(x))/x dx using u = ln(x) gives:
- In substitution, after finding ∫ f(u)du, we must:
- ∫ 2x·cos(x²) dx:
- ∫ eˣ/(1+eˣ) dx:
Question 1 of 250 correct so far