AP Calculus AB : Antiderivatives following directly from derivatives of basic functions

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #11 : Techniques Of Antidifferentiation

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Example Question #12 : Techniques Of Antidifferentiation

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Example Question #13 : Techniques Of Antidifferentiation

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Example Question #14 : Techniques Of Antidifferentiation

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Example Question #81 : Integrals

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Example Question #21 : Techniques Of Antidifferentiation

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Example Question #22 : Techniques Of Antidifferentiation

Given , find the general form for the antiderivative .

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To answer this, we will need to FOIL our function first.

Now can find the antiderivatives of each of these three summands using the power rule.

 (Don't forget )!

 

Example Question #23 : Techniques Of Antidifferentiation

Compute the following integral:

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Correct answer:

Explanation:

Compute the following integral:

Now, we need to recall a few rules.

1) 

2) 

3) 

4)

We can use all these rules to change our original function into its anti-derivative.

We can break this up into separate integrals for each term, and apply our rules individually.

The first two integrals can be found using rule 2

Next, let's tackle the middle integral:

Then the "sine" integral

And finally, the cosine integral.

Now, we can put all of this together to get:

Note that we only have 1 c, because the c is just a constant.

Example Question #24 : Techniques Of Antidifferentiation

Solve:

Possible Answers:

Correct answer:

Explanation:

The integral can be solved knowing the derivatives of the following functions:

Given that the integrand is simply the sum of these two derivatives, we find that our integral is equal to

Example Question #25 : Techniques Of Antidifferentiation

Solve:

Possible Answers:

None of the other answers

Correct answer:

None of the other answers

Explanation:

The integral is equal to

and was given by the following rule:

Using this rule becomes more clear when we rewrite the integral as

Note that because none of the answer choices had the integration constant C along with the proper integral result, the correct choice was "None of the other answers." Always check after solving an indefinite integral for C!

 

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