Grade 12 Calculus: Antidifferentiation Worksheet
A comprehensive worksheet for Grade 12 Calculus students focusing on antidifferentiation, including basic integrals, power rule, and applications.
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Grade 12 Calculus: Antidifferentiation Practice
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Read each question carefully and show all your work. Simplify your answers where possible.
Find the general antiderivative for each of the following functions:
1. f(x) = 3x²
2. f(x) = 5x³ - 2x + 1
Complete the following statements:
1. The antiderivative of xⁿ is + C, where n ≠ -1.
2. When finding an indefinite integral, we always add a of integration, denoted by C.
1. Which of the following is the antiderivative of f(x) = 4cos(x)?
4sin(x) + C
-4sin(x) + C
4cos(x) + C
-4cos(x) + C
2. If F'(x) = eˣ, what is F(x)?
xeˣ + C
eˣ + C
eˣ/x + C
ln(x) + C
Find the specific antiderivative F(x) satisfying the given conditions:
1. F'(x) = 6x² - 4x, F(0) = 5
2. F'(x) = sin(x), F(π) = 2
Determine if the following statements are true or false:
1. The antiderivative of a sum of functions is the sum of their antiderivatives.
True
False