Calculus 1 : Functions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #2163 : Calculus

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

In this problem we use a "u substitution" to account for the function inside of the parentheses. The steps for a "u-sub" are as follows:

1. Set the function equal to u, take the derivative of both sides, and solve for dx:

2. Substitute each of the x values for u values in the integral then solve accordingly:

3. Put the x values back into the equation and add "C" to get the final answer:

Example Question #91 : Equations

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 : 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 #1141 : Functions

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 #91 : Equations

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 : 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 #2172 : Calculus

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 #2173 : Calculus

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 : Writing Equations

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 : 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":

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