U-Substitution Calculus Worksheet
A Grade 12 Calculus worksheet focusing on integration using the u-substitution method with various problem types.
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U-Substitution Calculus Practice
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Read each problem carefully and use the u-substitution method to evaluate the definite or indefinite integral. Show all your work.
Evaluate the following indefinite integrals using u-substitution.
1. ∫ (2x + 1)³ dx
2. ∫ x√(x² + 5) dx
For the integral ∫ x sin(x²) dx, what would be the most appropriate choice for 'u'?
u = x
u = sin(x²)
u = x²
u = x sin(x²)
Evaluate the following definite integrals using u-substitution. Remember to change the limits of integration.
1. ∫ from 0 to 1 of x(x² + 1)³ dx
2. ∫ from 0 to π/2 of cos(x)e^(sin(x)) dx
Complete the following statements regarding u-substitution.
1. When performing u-substitution, the first step is typically to choose a suitable expression for u, usually the part of the integrand.
2. After choosing u, you must find du by u with respect to x.
3. For definite integrals, it is crucial to the limits of integration to be in terms of u.
Determine if the following statements are true or false.
1. U-substitution is a method used to integrate products of functions.
True
False
2. If u = x², then du = 2x dx.
True
False