Grade 12 Calculus: Antidifferentiation Worksheet
A comprehensive worksheet for Grade 12 Calculus students focusing on antidifferentiation, including basic integrals, power rule, and applications.
Includes
Standards
Topics
Grade 12 Calculus: Antidifferentiation Practice
Name:
Date:
Score:
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
Related Worksheets
Limits at Infinity Worksheet
This worksheet focuses on evaluating limits of functions as the variable approaches infinity, covering various techniques and function types relevant to Grade 12 Calculus.
Quotient Rule Practice Worksheet
A Grade 12 Calculus worksheet focusing on applying the quotient rule for differentiation.
Grade 12 Calculus: Related Rates Worksheet
A Grade 12 Calculus worksheet covering related rates problems, including applications in geometry and physics.
Taylor Series Exploration
A Grade 12 Calculus worksheet exploring Taylor series, focusing on definition, expansion, and common applications.
Particle Motion Calculus Worksheet
A Grade 12 Calculus worksheet focusing on particle motion, including displacement, velocity, acceleration, and interpreting motion graphs.
Lagrange Error Bound Worksheet
A Grade 12 Calculus worksheet focusing on understanding and applying the Lagrange Error Bound for Taylor polynomials.
U-Substitution Calculus Worksheet
A Grade 12 Calculus worksheet focusing on integration using the u-substitution method with various problem types.
Derivative Graphs Analysis
Analyze and interpret the graphs of functions and their derivatives, identifying key features such as increasing/decreasing intervals, local extrema, concavity, and points of inflection.