# Area of Surface of Revolution

1. Aug 3, 2009

### TheLegace

1. The problem statement, all variables and given/known data
Find area of surface generated by revolving about x-axis.

y=x^3/3 1<=x<=sqrt(7)

2. Relevant equations
find f'(x) = x^2

3. The attempt at a solution

A = integral[ (x^3/3) * [(1+(x^2)^2] ^(1/2) ] ]dx
= integral[ (x^3/3) * [(1+x^4) ^(1/2) ]dx
I just don't know where to go from here.

Any help is appreciated,
Thank You.

2. Aug 3, 2009

### Staff: Mentor

Ordinary substitution: let u = 1 + x^4.

I'm assuming that you have the correct integrand. If so, this substitution will help you out.

3. Aug 3, 2009

### nickmai123

You forgot the $$2\pi$$ in your equation, but you probably have that on paper. Here's what the integral should look like.

$$A=\frac{2\pi}{3}\int^{\sqrt{7}}_{1}{x^{3}\sqrt{1+x^{4}}dy$$

4. Aug 3, 2009

### TheLegace

Oh whoops, ok well having that in there, how could I continue this problem?

EDIT: I see how this can be solved, substition method.

Thank You.

Last edited: Aug 3, 2009
5. Aug 3, 2009

### nickmai123

Do what Mark44 said to do.

$$u=1+x^{4}$$

$$du=4x^{3}dx$$

Last edited: Aug 3, 2009
6. Aug 3, 2009

### Staff: Mentor

Make that du = 4x3dx

7. Aug 3, 2009

Haha oops.
The text passage contains a mathematical question related to finding the area of a surface of revolution, and it includes a discussion on how to solve the problem, but no final answer is provided.
single_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Area of Surface of Revolution

1. Aug 3, 2009

### TheLegace

1. The problem statement, all variables and given/known data
Find area of surface generated by revolving about x-axis.

y=x^3/3 1<=x<=sqrt(7)

2. Relevant equations
find f'(x) = x^2

3. The attempt at a solution

A = integral[ (x^3/3) * [(1+(x^2)^2] ^(1/2) ] ]dx
= integral[ (x^3/3) * [(1+x^4) ^(1/2) ]dx
I just don't know where to go from here.

Any help is appreciated,
Thank You.

2. Aug 3, 2009

### Staff: Mentor

Ordinary substitution: let u = 1 + x^4.

I'm assuming that you have the correct integrand. If so, this substitution will help you out.

3. Aug 3, 2009

### nickmai123

You forgot the $$2\pi$$ in your equation, but you probably have that on paper. Here's what the integral should look like.

$$A=\frac{2\pi}{3}\int^{\sqrt{7}}_{1}{x^{3}\sqrt{1+x^{4}}dy$$

4. Aug 3, 2009

### TheLegace

Oh whoops, ok well having that in there, how could I continue this problem?

EDIT: I see how this can be solved, substition method.

Thank You.

Last edited: Aug 3, 2009
5. Aug 3, 2009

### nickmai123

Do what Mark44 said to do.

$$u=1+x^{4}$$

$$du=4x^{3}dx$$

Last edited: Aug 3, 2009
6. Aug 3, 2009

### Staff: Mentor

Make that du = 4x3dx

7. Aug 3, 2009

Haha oops.
user
The text passage contains a mathematical question related to finding the area of a surface of revolution, and it includes a discussion on how to solve the problem, but no final answer is provided.

TYPE: SINGLE_QUESTION