Antidifferentiation Basics
This worksheet introduces fundamental concepts of antidifferentiation for Grade 9 students, focusing on finding antiderivatives of basic polynomial functions and understanding the constant of integration.
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Antidifferentiation Basics
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. What is the antiderivative of f(x) = 2x?
x²
2x²
x² + C
2x + C
2. The process of finding the antiderivative is also known as:
Differentiation
Integration
Factorization
Simplification
3. The antiderivative of a constant 'k' is .
4. When finding an indefinite integral, we always add a constant of integration, denoted by .
5. Find the antiderivative of f(x) = 3x².
6. Explain why there is always a constant of integration when finding an indefinite integral.
7. The derivative of x³ + 5 is 3x².
True
False
8. If F'(x) = f(x), then F(x) is an antiderivative of f(x).
True
False
Match the function with its antiderivative.
9. f(x) = 5
a. x³ + C
10. f(x) = x²
b. 5x + C
11. f(x) = 4x³
c. (1/3)x³ + C