U-Substitution Practice Worksheet

A Grade 11 Calculus worksheet focusing on U-substitution techniques for integration problems.

Grade 11 Math CalculusU-substitution

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Includes

3 Short AnswerFill in the BlanksMultiple ChoiceTrue / False

Standards

CCSS.MATH.CONTENT.HSF.IF.C.7CCSS.MATH.CONTENT.HSF.BF.B.4.A

Topics

CalculusU-substitutionIntegrationMathGrade 11

8 sections · Free to use · Printable

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