# Help with Volume of Revolution/Trig Substitution Problem

• student93
In summary, the conversation was about finding the volume of a solid using the disk method and trigonometric substitution. The problem was attached and the equations were provided. The student was having trouble simplifying the integral to get the answer of π/72.
student93

## Homework Statement

The problem is attached in this post.

## Homework Equations

The problem is attached in this post.

## The Attempt at a Solution

Disk method with the radius equal to x/((x^2+3)^5/4)

For Trig Substitution √(x^2+a^2) -> x=atanθ
a=√3 -> a^2=3
x=√(3)tanθ -> dx=√(3)sec^2(θ)
x^2=3tan^2(θ)Volume=π∫((3tan^2(θ)√(3)sec^2(θ))/(3tan^2(θ)+3)^5/4 from 0 to π/6

I can't seem to simplify the integral to the point where I can get the answer etc.

#### Attachments

• Screen shot 2014-02-24 at 1.55.53 AM.png
7.5 KB · Views: 514
hi student93!

(try using the X2 button just above the Reply box )

i haven't checked, it's too difficult to read , but you seem to have inserted an extra tanθ somewhere …

π∫((3tan(θ)√(3)sec2(θ))/(3tan2(θ)+3)5/4 can be simplified

## 1. What is the volume of revolution?

The volume of revolution is the volume of a three-dimensional shape formed by rotating a two-dimensional shape around an axis. It is commonly used in calculus to find the volume of irregular objects.

## 2. How do I find the volume of revolution using calculus?

To find the volume of revolution using calculus, you can use the disk or washer method, which involves integrating the cross-sectional areas of the shape being rotated. You can also use the shell method, which involves integrating the circumference of the shape being rotated.

## 3. What is trigonometric substitution?

Trigonometric substitution is a technique used in calculus to simplify integrals involving radical expressions. It involves replacing the variable in the integral with a trigonometric function, such as sine, cosine, or tangent, to make the integral easier to solve.

## 4. How do I use trigonometric substitution to solve a volume of revolution problem?

To use trigonometric substitution to solve a volume of revolution problem, you would first need to identify which trigonometric function to substitute for the variable in the integral. This is usually determined by the shape of the cross-sectional area being rotated. You would then substitute the trigonometric function and solve the resulting integral to find the volume.

## 5. Can I use trigonometric substitution for all volume of revolution problems?

No, trigonometric substitution is only useful for certain types of volume of revolution problems, specifically those involving radical expressions. It may not be applicable for other types of shapes or functions. It is important to carefully assess the problem before deciding to use trigonometric substitution.

• Calculus and Beyond Homework Help
Replies
9
Views
608
• Calculus and Beyond Homework Help
Replies
21
Views
2K
• Calculus and Beyond Homework Help
Replies
5
Views
1K
• Calculus and Beyond Homework Help
Replies
9
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
923
• Calculus and Beyond Homework Help
Replies
10
Views
737
• Calculus and Beyond Homework Help
Replies
14
Views
3K
• Calculus and Beyond Homework Help
Replies
3
Views
3K
• Calculus and Beyond Homework Help
Replies
2
Views
995
• Calculus and Beyond Homework Help
Replies
4
Views
960