Calculus 1 : How to find integral expressions

Study concepts, example questions & explanations for Calculus 1

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Example Questions

Example Question #81 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate the integral, use the inverse power rule:

Applying that rule 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:

Example Question #82 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate the integral, use the inverse power rule:

Applying that rule 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:

Example Question #83 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate the integral, use the inverse power rule:

Applying that rule to this problem gives us the following for the first term:

The following for the second term:

And the following for our thrid term:

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

Example Question #84 : Equations

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate the integral, use the inverse power rule:

Applying that rule to this problem gives us the following for the first term:

Add our "C" to get the final answer:

Example Question #84 : How To Find Integral Expressions

Evaluate the following indefinite integral:

Possible Answers:

Correct answer:

Explanation:

To evaluate this integral we have to remember the laws of trig functions. In this problem we also use a "u substitution" to account for the function inside of the cosine. The steps for a "u-sub" are as follows:

1. Set the function equal to u and take the derivative of both sides.

 

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

3. Put the x values back into the equation to get the final answer:

 

 

Example Question #85 : How To Find Integral Expressions

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 #86 : How To Find Integral Expressions

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 #87 : How To Find Integral Expressions

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 #88 : How To Find Integral Expressions

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 #89 : How To Find Integral Expressions

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:

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