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

Click For Summary
SUMMARY

The volume of the solid formed in the first quadrant by the curves y=x^4 and y=125x when rotated around the x-axis can be computed using the washer method. The integral limits are established from 0 to 5. The correct integral to evaluate is π times the difference of the squares of the outer and inner radii, specifically π∫[0 to 5] ((125x)^2 - (x^4)^2) dx. Previous attempts using the disk method were incorrect, emphasizing the necessity of applying the washer method for this problem.

PREREQUISITES
  • Understanding of calculus concepts, specifically integration
  • Familiarity with the washer method for volume calculation
  • Knowledge of polynomial functions and their graphs
  • Ability to evaluate definite integrals
NEXT STEPS
  • Study the washer method in detail for calculating volumes of solids of revolution
  • Practice evaluating definite integrals involving polynomial functions
  • Learn about the geometric interpretation of integrals in volume calculations
  • Explore examples of volume calculations using both disk and washer methods
USEFUL FOR

Students studying calculus, particularly those focusing on volume calculations of solids of revolution, as well as educators looking for examples to illustrate the washer method.

anonom30
Messages
1
Reaction score
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.
 
Physics news on Phys.org
I do not think this can be solved by "disks"...try washer method

Casey
 

Similar threads

Volume of a solid of revolution around the y-axis (def. integration)
  • · Replies 3 ·
Replies
3
Views
2K
Area surface of revolution (rotating this astroid curve around the x-axis)
  • · Replies 2 ·
Replies
2
Views
3K
Volume of revolution, region bounded by two functions
  • · Replies 1 ·
Replies
1
Views
2K
Volume of Static Solid Using Cross-Sectional Area (Integration)
  • · Replies 2 ·
Replies
2
Views
1K
Volume of revolution around the y-axis
  • · Replies 20 ·
Replies
20
Views
3K
Volume of revolution in the first quadrant?
  • · Replies 3 ·
Replies
3
Views
3K
Volume between a region (above x-axis and below parabola) and a surface
  • · Replies 4 ·
Replies
4
Views
3K
Solids of Revolution defined by inequalities
  • · Replies 11 ·
Replies
11
Views
2K
Volume of Revolution: Find V with Shell Method
  • · Replies 13 ·
Replies
13
Views
2K
Triple Integral To Find Volume Between Cylinder And Sphere
  • · Replies 2 ·
Replies
2
Views
2K