Grade 12 Integration Worksheet
A comprehensive worksheet for Grade 12 Calculus students focusing on various integration techniques and applications.
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Standards
Topics
Grade 12 Integration Practice
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Date:
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Read each question carefully and show all your work. Use proper notation for all integration problems. Simplify your answers where possible.
1. Evaluate the following indefinite integral: ∫ (3x² - 2x + 5) dx
2. Evaluate the definite integral: ∫ from 1 to 3 of (x³ + 2x) dx
3. Which substitution would be most appropriate for evaluating ∫ x(x² + 1)⁵ dx?
u = x
u = x²
u = x² + 1
u = (x² + 1)⁵
4. Find the area under the curve y = x² from x = 0 to x = 2.
5. The Fundamental Theorem of Calculus states that if F'(x) = f(x), then ∫ from a to b of f(x) dx = F( ) - F( ).
6. True or False: ∫ [f(x) + g(x)] dx = ∫ f(x) dx + ∫ g(x) dx
True
False
7. Set up, but do not evaluate, the integral for ∫ x cos(x) dx using integration by parts.
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