How Do You Calculate the Volume of a Solid Rotated Around x=2?

[joe007]

Volume Of solids question help!

Homework Statement

i) find the area enclosed by the curves y=x^1/2 and y=x^4
ii)find the volume of the solid when the area in part (i) is rotated about the the line x=2

Homework Equations

V=PI*y^2dx

The Attempt at a Solution

wel the area is simple integral 0 to1 root x -x^.5 and i got 7/15

but I am not sure how to calculate the volume about x=2

 

[tiny-tim]

hi joe007!

ii)find the volume of the solid when the area in part (i) is rotated about the the line x=2

slice the volume into horizontal "washers" of height dy, and integrate

 

[HallsofIvy]

Equivalent to "washers": Use "disks" to find the volume when y= x^{1/2} is rotated around the x-axis, then use "disks" to find the volume when y= x^4 is rotated around the x-axis, and subtract.

 

[joe007]

so its V=2PI* (integral 0 to 2) (x-2)x^0.5 -(x-2)x^4 dx

 

[joe007]

i think it should be from 0 to 1

 

[SammyS]

i think it should be from 0 to 1

Correct !