What is the integral of $$x^{-n}$$ ?

For n ≠ 1, $$\int x^{-n} \, dx = \frac{x^{-n+1}}{-n+1} + C$$ .

What is the integral of sin(x)?

$$\int \sin(x) \, dx = -\cos(x) + C$$ .

What is the integral of cos(x)?

$$\int \cos(x) \, dx = \sin(x) + C$$ .

What is the integral of 1/x?

$$\int \frac{1}{x} \, dx = \ln|x| + C$$ .

What is the integral of a sum of functions?

$$\int (f(x) + g(x)) \, dx = \int f(x) \, dx + \int g(x) \, dx + C$$ .

What is the integral of a product of a constant and a function?

$$\int k \, f(x) \, dx = k \int f(x) \, dx + C$$ .

What is the integral of a polynomial function?

For a polynomial $$f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_0$$ , the integral is $$\int f(x) \, dx = \frac{a_n}{n+1} x^{n+1} + \frac{a_{n-1}}{n} x^n + ... + a_0 x + C$$ .

4.1 - 4.4 Review Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the indefinite integral of 4 with respect to x?

Back

4x + C

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What is the indefinite integral of dx?

Back

x + C

4.

FLASHCARD QUESTION

Front

Another word for 'integral' is?

Back

Antiderivative

5.

FLASHCARD QUESTION

Front

What is the integral of a constant function?

Back

6.

FLASHCARD QUESTION

Front

What is the Fundamental Theorem of Calculus?

Back

7.

FLASHCARD QUESTION

Front

What is the power rule for integration?

Back

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