AP Calculus AB : Asymptotic and Unbounded Behavior

Study concepts, example questions & explanations for AP Calculus AB

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Example Questions

Example Question #41 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

 

Correct answer:

 

Explanation:

We evaluate the integral according to this equation:

. From this, we acquire the answer above. Keep in mind that  is the same as .  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #42 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

First, we remember that the integral of a sum is the same as the sum of the integrals, so we can split the sum into seperate integrals and solve them individually.  We then evaluate each integral according to this equation:

. From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #43 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

First, we know that we can pull the constant  out of the integral, and we then evaluate the integral according to this equation:

. From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #44 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

First, we know that we can pull the constant  out of the integral, and we then evaluate the integral according to this equation:

. From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #45 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

We evaluate the integral according to this equation:

. Keep in mind that  is the same as . From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #46 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

We know that the derivative of  and the integral of .  We must remember the chain rule and therefore keep the 2 in the exponent. From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #47 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

First, we know that we can pull the constant  out of the integral, and we then evaluate the integral according to this equation:

. From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #48 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

For this problem, we must simply remember that the integral of  is , just like how the derivative of  is .  Just keep in mind that we need that constant of integration  that would have been lost during differentiation.

Example Question #49 : Asymptotic And Unbounded Behavior

Evaluate the following indefinite integral.

Possible Answers:

Correct answer:

Explanation:

First, we know that we can pull the constant  out of the integral, and we then evaluate the integral according to this equation:

. From this, we acquire the answer above.  As a note, we cannot forget the constant of integration  which would be lost during the differentiation.

Example Question #50 : Asymptotic And Unbounded Behavior

Possible Answers:

\frac{1}{2}sec^2xtanx +C

Correct answer:

Explanation:

The answer is . The definition of the derivative of  is . Remember to add the  to undefined integrals.

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