U-Substitution Practice Worksheet
Practice problems for U-substitution in calculus, covering basic definite and indefinite integrals.
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U-Substitution Practice Worksheet
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Read each problem carefully and use the method of U-substitution to find the integral. Show all your work for full credit.
1. Evaluate the indefinite integral: ∫ (2x + 1)³ dx
2. Find ∫ x√(x² + 5) dx
3. Calculate ∫ e^(4x) dx
4. Evaluate ∫ sin(3x) dx
5. Evaluate the definite integral: ∫ from 0 to 1 of x(x² + 1)³ dx
6. Find ∫ from 0 to π/2 of cos(x)e^(sin(x)) dx
For each integral, identify a suitable 'u' for U-substitution:
7. ∫ (x³ + 2)² * 3x² dx Let u =
8. ∫ sec²(5x) dx Let u =
9. ∫ (ln x) / x dx Let u =
10. When performing U-substitution for a definite integral, the limits of integration must also be changed to be in terms of u.
True
False
11. U-substitution is always applicable for any integral.
True
False