17 Questions
What is the process of passing from the derivative of a function to the function itself?
Antidifferentiation
What symbol denotes the operation of antidifferentiation?
∫
What is the function f called in the context of antidifferentiation?
The integrand
What is the expression F(x) + C called?
The general antiderivative
What does dx help identify in an integral?
The variable of integration
What is the relationship between integration and differentiation?
They are opposite operations
What is the formula for the power rule in integral calculus?
∫ 𝑥 𝑛 𝑑𝑥 = 𝑥 𝑛+1 𝑛+1 +C
What is the condition for the power rule to be applied?
n ≠ −1
What is the result of differentiating 𝑥 𝑛+1 𝑛+1 +C?
𝑥 𝑛
What is the formula for the antiderivative of (ax + b)𝑛?
1 𝑎(𝑛+1) (ax + b)𝑛+1 + 𝐶
What is the result of applying the power rule to ∫(2𝑥 − 1)3 𝑑𝑥?
1 8 (2𝑥 − 1)4 + 𝐶
What is the result of applying the power rule to ∫ 𝑡 3 𝑑𝑡?
2 𝑡 4 + 𝐶
What is the term for the function F(x) in the equation ∫f(x)dx = F(x) + C?
Antiderivative
What is the value of the derivative of a constant?
0
What is the formula for the indefinite integral of x^n?
∫x^n dx = x^(n+1) / (n+1) + C
What is the term for the constant C in the equation ∫f(x)dx = F(x) + C?
Constant of Integration
What is the antiderivative of f(x) = 2x?
x^2 + C
Test your knowledge of calculus with this quiz on integrals and antiderivatives. Learn how to find the antiderivative of a function and understand the concept of the constant of integration.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
