How to Compute the Volume of a Solid of Revolution Between y=x^4 and y=125x?

They have found the integral's limits to be from 0 to 5, but are unsure of what to integrate. They have tried integrating both (x^4 - 125x)^2 and (125x - x^4)^2, but have yielded the same incorrect answer. They also attempted to integrate (125x)^2 from 0 to 5, but found this to be incorrect as well. In summary, Casey believes that this problem cannot be solved using the disk method and suggests trying the washer method instead.
  • #1
anonom30
1
0

Homework Statement



Compute the volume of the solid formed in the first quadrant by y=x^4 and y=125x
when rotated around the x axis.


Homework Equations



the integral for a disk is solved by taking the integral from a to b of pi R^2

The Attempt at a Solution



I found the integral's limits to be from 0 to 5. My problem is figuring out what to actually integrate. I have tried integrating both (x^4 - 125x)^2 and (125x - x^4)^2 with both yielding the same wrong answer. I then tried doing the integral for (125x)^2 from 0 to 5 and found that to be wrong also.
 
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  • #2
I do not think this can be solved by "disks"...try washer method

Casey
 

FAQ: How to Compute the Volume of a Solid of Revolution Between y=x^4 and y=125x?

What is revolution using disk method?

Revolution using disk method is a mathematical technique used to find the volume of a three-dimensional object that is formed by rotating a two-dimensional shape around an axis. This method involves dividing the object into thin disks and adding up the volumes of these disks to get the total volume of the object.

How is the axis determined in revolution using disk method?

The axis in revolution using disk method is usually a line or curve around which the two-dimensional shape is rotated. This axis can be either vertical or horizontal, depending on the orientation of the object being rotated. It is important to choose the correct axis in order to accurately calculate the volume of the object.

What are the steps involved in using revolution using disk method?

The first step is to sketch the two-dimensional shape that will be rotated. Then, determine the axis of rotation and the limits of integration. Next, divide the shape into thin disks and calculate the volume of each disk using the formula V = πr²h, where r is the radius of the disk and h is its height. Finally, add up the volumes of all the disks to get the total volume of the object.

Can revolution using disk method be used for any shape?

No, revolution using disk method is only applicable to shapes that can be rotated around a single axis. Examples of such shapes include circles, rectangles, and triangles. Shapes with irregular curves may require more complex methods, such as the shell method or the washer method, to find their volumes.

What are the limitations of revolution using disk method?

Revolution using disk method is limited to finding the volume of objects with a single axis of revolution. Additionally, this method can only be used for objects with a uniform cross-section, meaning that the shape of the object remains the same throughout the rotation. Objects with varying cross-sections may require alternative methods for calculating their volumes.

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