Solve Volume of Revolution (VOR) for x^2+y^2=25|Definite Integrals

  • Thread starter john.duke10
  • Start date
  • Tags
    Revolution
In summary, the formula for calculating the volume of revolution is V = π∫(R(x))^2 dx. The limits of integration for VOR are determined by setting the given equation equal to the variable of integration and solving for the corresponding y-values. VOR can be used for any shape that can be formed by rotating a function around the x-axis. It is typically used for definite integrals, but can also be used for indefinite integrals. However, it has limitations when the shape being rotated intersects with the axis of revolution and assumes a continuous and defined shape. In these cases, alternative methods should be used.
  • #1
john.duke10
3
0
help my final is friday and law school depends upon it.volume of revolution (VOR) for base of x^2 + y^2=25. Assume the square slcies are Peripindxular to the x axis.

voR for area between y=2x and y=2cos x revlved aroung the line y=-50

write definite integrals and evaluate

thanks in advance
 
Physics news on Phys.org
  • #2
Nope. Can't do it. At least TRY! People will help with a wrong attempt. They won't work your homework for you. And I'm not sure a failure to enter law school will elicit much sympathy.
 

FAQ: Solve Volume of Revolution (VOR) for x^2+y^2=25|Definite Integrals

What is the formula for calculating the volume of revolution?

The formula for calculating the volume of revolution is V = π∫(R(x))^2 dx, where R(x) is the radius of the cross-sectional area at a given x-value.

How do I determine the limits of integration for VOR?

The limits of integration for VOR are determined by setting the given equation equal to the variable of integration (in this case, x) and solving for the corresponding y-values. These y-values will be the upper and lower limits of integration.

Can I use VOR for any shape?

VOR can be used for any shape that can be formed by rotating a function around the x-axis. This includes circles, squares, rectangles, and more complex shapes.

Can VOR be used for both definite and indefinite integrals?

VOR is typically used for definite integrals, as it requires specific limits of integration. However, it is possible to use it for indefinite integrals by setting the lower limit of integration to a constant and the upper limit to x. This will result in a general equation for the volume of revolution.

Are there any limitations to using VOR?

VOR has limitations when the shape being rotated intersects with the axis of revolution. In these cases, a different method, such as the disk or washer method, should be used. VOR also assumes that the shape being rotated is continuous and has a defined upper and lower bound.

Similar threads

Volume of revolution, region bounded by two functions
Replies
1
Views
1K
Volume of Static Solid Using Cross-Sectional Area (Integration)
Replies
2
Views
749
Volume of a solid of revolution around the y-axis (def. integration)
Replies
3
Views
1K
Volume of revolution in the first quadrant?
Replies
3
Views
3K
Volume of revolution around the y-axis
Replies
20
Views
2K
Volume integral of x^2 + (y-2)^2 +z^2 = 4 where x , y , z > 0
Replies
21
Views
2K
Volumes of Revolution Question
Replies
3
Views
1K
I Volume of Solid of Revolution (About the line y = x)
Replies
6
Views
2K
Solve p = P(2X <= Y^2) using double integral
Replies
4
Views
1K
Volume of Solid of Revolution for y=x^2-2, y=0 about y=-1
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top