Christopher Xu
New member
Hmm, another one of these is giving me a little trouble. For some reason, I've got some difficulties when it comes to rotating these things across the axises I'm not used to.
So anyways, use the shell method to find the volume of the solid generated by revolving it about the x-axis. The equation is x^2 = 4y, y = 4.
Since this is the shell method, I need to write it in terms of 2pi * integral of y=0 to y=4 of f
* y.
So, I need to solve for f. I square root both sides so that x = sqrt(4y). (Do I need to include the negative sign too?)
Then, it's a matter of plugging in stuff and integrating.
2pi * integral from 0 to 4 of sqrt(4y) * y
= 2pi * integral from 0 to 4 of 2y^(3/2)
= 2pi * |(4y^(5/2))/5| from 0 to 4
= 2pi * 25.6
= 51.2pi
Look right?
intc_escapee, I'm pretty sure you're correct (I got the same with the disc method; was wondering which of mine was wrong), but I'm not entirely certain how you got ? 4y?y dy when the form is ? f*y dy.
Edit 2: I thought the width of the shell was sqrt(4y), though, and not 4sqrt? Is this just because I'm not taking into account the negative part of the equation or something?
I'll give you the points in a minute; gonna fiddle around with this and see what obvious thing I'm forgetting.
So anyways, use the shell method to find the volume of the solid generated by revolving it about the x-axis. The equation is x^2 = 4y, y = 4.
Since this is the shell method, I need to write it in terms of 2pi * integral of y=0 to y=4 of f
* y.So, I need to solve for f
. I square root both sides so that x = sqrt(4y). (Do I need to include the negative sign too?)Then, it's a matter of plugging in stuff and integrating.
2pi * integral from 0 to 4 of sqrt(4y) * y
= 2pi * integral from 0 to 4 of 2y^(3/2)
= 2pi * |(4y^(5/2))/5| from 0 to 4
= 2pi * 25.6
= 51.2pi
Look right?
intc_escapee, I'm pretty sure you're correct (I got the same with the disc method; was wondering which of mine was wrong), but I'm not entirely certain how you got ? 4y?y dy when the form is ? f
*y dy.Edit 2: I thought the width of the shell was sqrt(4y), though, and not 4sqrt
? Is this just because I'm not taking into account the negative part of the equation or something?I'll give you the points in a minute; gonna fiddle around with this and see what obvious thing I'm forgetting.