Calculus 1 : How to find integral expressions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #91 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

 

Example Question #92 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. We also need to remember our properties of trig functions. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

Example Question #93 : Equations

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, all we have to remember is that the integral of e doesn't change. That gives us the following:

Example Question #93 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

Example Question #94 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

Example Question #95 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this integral, we use the power rule for the first term:

And use the laws of trig functions for the second term:

We can combine these terms and add our "C" to get the final answer:

Example Question #96 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

Example Question #97 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

Example Question #98 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this problem we have to use a u substitution. A "u-sub" is done by using the following steps:

1. Set u equal to the x equation in parentheses, take the derivative, and solve:

2. Replace x values with u values and integrate accordingly:

3. Put the original x equation back in for u and add "C":

Example Question #99 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To solve this integral, use the power rule. Applying it to this problem gives us the following for the first term:

And the following for the second term:

We can combine these terms and add our "C" to get the final answer:

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