Surface Area Problem: Rotating y=x^4/16+1/2x^2 About Y-Axis

Thread starter temaire
Start date Mar 2, 2010
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Area Surface Surface area

In summary, the formula for calculating the surface area of a solid of revolution is 2π∫(y√(1+(dy/dx)^2)dx) for rotating about the x-axis and 2π∫(x√(1+(dx/dy)^2)dy) for rotating about the y-axis. The limits of integration can be determined by setting the function being rotated equal to 0 and solving for the corresponding values of x or y. A solid of revolution is a three-dimensional object generated by rotating a two-dimensional shape around an axis, and the surface area can be calculated using the mentioned formula. The problem of rotating y=x^4/16+1/2x^2 about the

Mar 2, 2010

temaire

Homework Statement
Find the surface area obtained by rotating the curve [tex]y = \frac{x^4}{16} + \frac{1}{2x^2}[/tex] 1 < x < 2 about the y-axis.

The attempt at a solution
http://img341.imageshack.us/img341/3245/mathy.jpg

My final answer is [tex]\frac{41\pi}{10}[/tex]. Is this correct?

Last edited by a moderator: May 4, 2017

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Mar 2, 2010

Char. Limit

Gold Member

Seems right to me.

FAQ: Surface Area Problem: Rotating y=x^4/16+1/2x^2 About Y-Axis

What is the formula for calculating the surface area of a solid of revolution?

The formula for calculating the surface area of a solid of revolution is 2π∫(y√(1+(dy/dx)^2)dx), where y is the function being rotated and dy/dx represents the derivative of y with respect to x.

How do you find the surface area of a solid of revolution when rotating about the y-axis?

When rotating about the y-axis, the formula for surface area becomes 2π∫(x√(1+(dx/dy)^2)dy), where x is the function being rotated and dx/dy represents the derivative of x with respect to y.

How do you determine the limits of integration for finding the surface area of a solid of revolution?

The limits of integration for finding the surface area of a solid of revolution can be determined by setting the function being rotated equal to 0 and solving for the corresponding values of x or y. These values will serve as the lower and upper limits of integration, depending on the orientation of the axis of rotation.

Can you explain the concept of a solid of revolution?

A solid of revolution is a three-dimensional object generated by rotating a two-dimensional shape around an axis. The resulting solid is symmetrical and has a circular cross-section. The surface area of a solid of revolution can be calculated using the formula mentioned in the previous questions.

What is the significance of the surface area problem involving rotating y=x^4/16+1/2x^2 about the y-axis?

The surface area problem involving rotating y=x^4/16+1/2x^2 about the y-axis is significant as it represents a common application of the concept of solids of revolution in mathematics. It also helps to understand the relationship between the function being rotated and the resulting surface area, as well as the importance of correctly setting the limits of integration in the calculation process.