Integration by substitution
Grade 12 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Esme wants a substitution for ∫ 2x(x² + 1)⁵ dx. Which u and du make it a basic integral?
- u = 2x, du = 2 dx
- u = x² + 1, du = 2x dx
- u = x² + 1, du = 2x² dx
Jun wants a substitution for ∫ 3x²√(x³ + 4) dx. Which u and du make it a basic integral?
- u = x³ + 4, du = 3x³ dx
- u = x³ + 4, du = 3x² dx
- u = 3x², du = 6x dx
Kira wants a substitution for ∫ (2x + 3)(x² + 3x)⁴ dx. Which u and du make it a basic integral?
- u = x² + 3x, du = (2x + 3x) dx
- u = x² + 3x, du = (2x + 3) dx
- u = 2x + 3, du = 2 dx
Luz wants a substitution for ∫ cos x · e^(sin x) dx. Which u and du make it a basic integral?
- u = cos x, du = −sin x dx
- u = sin x, du = cos x dx
- u = sin x, du = −cos x dx
Noah writes ∫ x(x² + 5)⁴ dx = a(x² + 5)⁵ + C. What is a?
Ren writes ∫ x(x² + 2)⁵ dx = a(x² + 2)⁶ + C. What is a?
Zee writes ∫ x(x² + 7)² dx = a(x² + 7)³ + C. What is a?
Tala substitutes u = x² + 1 in ∫ from 0 to 2 of 2x(x² + 1)³ dx. What is the new upper limit for u?
Pia substitutes u = x² + 4 in ∫ from 0 to 3 of 2x(x² + 4)³ dx. What is the new upper limit for u?
Esme substitutes u = x² + 2 in ∫ from 0 to 4 of 2x(x² + 2)³ dx. What is the new upper limit for u?