What is the antiderivative of $$f(x)=0$$ ?

$$F(x)=C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\text{sin}(x)$$ ?

$$F(x)=-\text{cos}(x)+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\frac{1}{x\text{sqrt}(x^2-1)}$$ , where |x|>1?

$$F(x)=\text{sec}^{-1}(x)+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\frac{1}{1+x^2}$$ ?

$$F(x)=\text{tan}^{-1}(x)+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\frac{-1}{1+x^2}$$ ?

$$F(x)=-\text{cot}^{-1}(x)+C$$ , where C is a constant.

What is the constant of integration?

The constant of integration (C) represents an infinite number of antiderivatives for a given function.

What is the antiderivative of $$f(x)=k$$ , where k is a constant?

$$F(x)=kx+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=e^x$$ ?

$$F(x)=e^x+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=x^n$$ , where n ≠ -1?

$$F(x)=\frac{x^{n+1}}{n+1}+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\text{cos}(x)$$ ?

$$F(x)=\text{sin}(x)+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\text{sec}^2(x)$$ ?

$$F(x)=\text{tan}(x)+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\text{csc}^2(x)$$ ?

$$F(x)=-\text{cot}(x)+C$$ , where C is a constant.

What is the antiderivative of $$f(x)=\text{sin}^2(x)$$ ?

$$F(x)=\frac{1}{2}(x - \text{sin}(x)\text{cos}(x)) + C$$ , where C is a constant.

AP Calculus - Antiderivatives Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

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3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

Front

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6.

FLASHCARD QUESTION

Front

Define an antiderivative.

Back

An antiderivative of a function f(x) is a function F(x) such that F'(x) = f(x).

7.

FLASHCARD QUESTION

Front

What is the relationship between differentiation and antiderivatives?

Back

Differentiation is the process of finding the derivative, while finding an antiderivative is the reverse process.

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