Chapter 4 - Antiderivative Flashcards

1
Q

What is an Antiderivative?

A

A function F is called antiderivative of f on an interval I IF F’(X) = f(x) for all x in I

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2
Q

What is the Antiderivative Theorem?

A

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is..

F(x) + C

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3
Q

What is the antiderivative of cf(x)?

A

cF(x)

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4
Q

what is the antiderivative of f(x) + g(x)?

A

F(x) + G(x)

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5
Q

what is the antiderivative of X^n (n cannot equal 1)?

A

X^(n+1)/n +1

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6
Q

What is the antiderivative of (1/x)?

A

ln|x|

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7
Q

What is the antiderivative of e^x?

A

e^x/(derivative of x) + C

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8
Q

what is the antiderivative of cos(x)?

A

sin(x)

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9
Q

What is the antiderivative of sin(x)?

A

-cos(x)

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10
Q

What is the antiderivative of sec^2(x)?

A

tan(x)

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11
Q

What is the antiderivative of sec(x)tan(x) ?

A

sec(x)

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12
Q

What is the antiderivative of 1/√ (1 - x^2)?

A

arcsin(x)

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13
Q

What is the antiderivative of 1/√ (1 + ^2) ?

A

arctan(x)

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14
Q

What is the antiderivative of cosh(x) ?

A

sinh(x)

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15
Q

what is the antiderivative of sinh(x) ?

A

cosh(x)

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