U-Substitution Practice Worksheet
A Grade 11 Calculus worksheet focusing on U-substitution techniques for integration problems.
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U-Substitution Practice
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Read each problem carefully and use the method of U-substitution to evaluate the given integrals. Show all your work for full credit.
1. Evaluate the integral: ∫ (2x + 1)⁵ dx
2. Evaluate the integral: ∫ x²√(x³ + 1) dx
For the integral ∫ cos(3x) dx, let u = and du = .
For the integral ∫ e^(x²) * 2x dx, let u = and du = .
3. Which substitution would be most appropriate for evaluating ∫ x * sin(x²) dx?
u = x
u = sin(x²)
u = x²
u = x * sin(x²)
4. Evaluate the definite integral: ∫ from 0 to 1 of x * e^(x²) dx
5. When performing U-substitution for a definite integral, it is necessary to change the limits of integration.
True
False
6. Evaluate the integral: ∫ x / √(1 - x²) dx
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