Integration by substitution
Grade 12 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
Esme writes ∫ x(3x² + 1)³ dx = (3x² + 1)⁴/N + C. What is N?
Jun writes ∫ x(4x² + 5)² dx = (4x² + 5)³/N + C. What is N?
Kira writes ∫ x(5x² + 2)³ dx = (5x² + 2)⁴/N + C. What is N?
Luz writes ∫ x(2x² + 7)⁴ dx = (2x² + 7)⁵/N + C. What is N?
Noah evaluates ∫ from 0 to π/2 of cos x sin³ x dx with u = sin x. What is it?
Ren evaluates ∫ from 0 to π/2 of cos x sin⁴ x dx with u = sin x. What is it?
Zee evaluates ∫ from 0 to π/2 of cos x sin⁵ x dx with u = sin x. What is it?
Which substitution turns ∫ 4x³(x⁴ − 2)⁶ dx into a basic integral in u, for Tala?
- u = 4x³, du = 12x² dx
- u = x, du = dx
- u = x⁴ − 2, du = 4x³ dx
Which substitution turns ∫ e^(√x)/√x dx into a basic integral in u, for Pia?
- u = 1/√x, du = −dx/(2x√x)
- u = √x, du = dx/(2√x)
- u = x, du = dx
Which substitution turns ∫ x/(x² + 9) dx into a basic integral in u, for Esme?
- u = 2x, du = 2 dx, so x = u/2
- u = x, du = dx
- u = x² + 9, du = 2x dx