calc_tutorial_5_7_044

Problem Statement

{3,5,7}

{2,4,8}

2*5

4*8

2*8

Calculate the integral.

Step 1

Question Sequence

Question 1

In order to use a substitution, rewrite in terms of sine and cosine.

A.

B.

Correct.

Incorrect.

Step 2

Since the numerator is the derivative of the denominator, except for a constant factor, the substitution form of the integrand is , where a is a constant factor.

Question Sequence

Question 2

Use the substitution

A.

B.

C.

D.

Find du.

A.

B.

C.

D.

Incorrect. Do you see where you went wrong?

Excellent work.

Step 3

Question Sequence

Question 3

Substitute the expressions for u and for du to write in terms of u.

A.

B.

C.

D.

Incorrect. Do you see where you went wrong?

Excellent work.

Step 4

Question Sequence

Question 4

Evaluate the indefinite integral in terms of u. (Use C for the constant of integration. Remember to use ln |u| where appropriate.)

A.

B.

C.

D.

Incorrect. Do you see where you went wrong?

Excellent work.

Step 5

Question Sequence

Question 5

Substitute in to determine the given integral in terms of x.

A.

B.

C.

D.

Incorrect. Do you see where you went wrong?

Excellent work.