Chapter 1. Title

1.1 Problem Statement

{2,3,4,5}

pow($a,2)

(pow($a,3)+pow($c,3))/3-pow($c,2)+$a*$c

Write the integral as a sum of integrals without absolute values and evaluate.

1.2 Step 1

To eliminate the absolute values and solve the integral, we need to determine where the expression inside the absolute value is nonpositive and where the expression inside the absolute value is nonnegative inside our limits of integration.

Question Sequence

Question 1.1

For 1Wh3cvJ2xF4=

Therefore we can eliminate the absolute value sign when we restrict within those intervals.

Rewrite without absolute value signs on the restricted intervals.

For

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

For

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

Use this information to write the integral as a sum of two integrals without absolute values.

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

Correct.

That's not right. Check your work.

Incorrect.

1.3 Step 2

In order to evaluate the integral, we will need antiderivatives for each of the integrands in the two integrands without absolute values.

Question Sequence

Question 1.2

Find an antiderivative F(x) for .

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

Find an antiderivative G(x) for

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

Incorrect. Do you see where you went wrong?

Excellent work.

1.4 Step 3

Question Sequence

Question 1.3

Use the Fundamental Theorem of Calculus, Part 1, and the antiderivatives found in step 2 to evaluate. Round your answer to three decimal places.

qjqZz1N+poo=

Incorrect. Do you see where you went wrong?

Excellent work.