Title

Problem Statement

{2,3,4,5}

pow(2,2)

(pow(2,3)+pow(4,3))/3-pow(4,2)+2*4

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

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

For

For

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

Rewrite without absolute value signs on the restricted intervals.

For

A.

B.

For

A.

B.

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

A.

B.

Correct.

That's not right. Check your work.

Incorrect.

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 2

Find an antiderivative F(x) for .

A.

B.

Find an antiderivative G(x) for

A.

B.

Incorrect. Do you see where you went wrong?

Excellent work.

Step 3

Question Sequence

Question 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.

Incorrect. Do you see where you went wrong?

Excellent work.