Integral problem with A and c. im very confused, help would be welcomed :)

Sep 2016
2
0
Rochester, New York
This is the question and I'm not entirely sure where to go from here. Thanks!

Assume [FONT=MathJax_Math]c[/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]0[/FONT] and A>0, and compute the volume of the solid obtained by revolving the region bound by the graph of f(x)=Ax^2, the vertical line x=c, and the x-axis about the x-axis. Your answer should be in terms of A and c. [FONT=MathJax_Math]c[/FONT]
 

romsek

MHF Helper
Nov 2013
6,838
3,079
California
This is the question and I'm not entirely sure where to go from here. Thanks!

Assume [FONT=MathJax_Math]c[/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]0[/FONT] and A>0, and compute the volume of the solid obtained by revolving the region bound by the graph of f(x)=Ax^2, the vertical line x=c, and the x-axis about the x-axis. Your answer should be in terms of A and c. [FONT=MathJax_Math]c[/FONT]
imagine chopping this volume up into disks along the x axis.

each disk has a radius $r(x)$ and a thickness $dx$

the volume of each disk is given by $dV = \pi \left(r(x)\right)^2 ~dx$

$r(x) =$
$A x^2$

we integrate these differential volumes to find the entire volume

$V = \displaystyle{\int_0^c}\pi \left(A x^2\right)^2~dx = \displaystyle{\int_0^c}\pi A^2 x^4 ~dx=\dfrac{\pi A^2 c^5}{5} $
 
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Debsta

MHF Helper
Oct 2009
1,363
635
Brisbane
Could you do the question if A and c were specific numbers?
 
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