Calculus
posted by Becca .
Find the volume of the solid formed when the region bounded by y=3x^2 and y=36x^2 is revolved about the xaxis.

I see several posts made by you dealing mainly with these integrations problems, without any indication by you showing any steps or attempts.
I will do this one. Try to follow these steps to solve the others
Make a sketchl
First you need the intersection to see the region that you are revolving.
y = 3x^2 and y = 36x^2
3x^2 = 36x^2
4x^2 = 36
x = ± 3
Because of the symmetry, I will boundaries from 0 to 3, then double our volume
in general,
Volume = π∫y^2 dx from left boundary to right boundary
the y , the height or radius of our rotation, is
36x^2  3x^2 = 364x^2
V = 2π∫ (364x^2)^2 dx from 0 to 3
= 2π∫ (1296  288x^2 + 16x^4) dx from 0 to 3
= 2π [ 1296x  96x^3 + (16/5)x^5] from 0 to 3
= 2π (3888  2592 + 3888/5  0  0  0)
= (20736/5)π = appr. 13028.8 
I use this to check my answers. I apologize for not realizing that I should have proven to you that I was doing them by myself at first.

Fair enough.
In that case, you should post the answer you got, that way I can just do some fast scribbling on a piece of scrap paper and either confirm or reject your answer.
It would save us a lot of unnecessary typing of the whole solution.
Respond to this Question
Similar Questions

calculus 2
The region bounded by y=e^(x^2),y=0 ,x=0 ,x=1 and is revolved about the yaxis. Find the volume of the resulting solid. 
Calculus
This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of … 
calculus
Let R be the region in the first quadrant bounded by the graphs of y=e^x, y=1/2x+1, and x=2. Then find the volume of the solid when R is revolved about each of the following lines... the x axis, y=1, y=2, the y axis, x=1, and x=3. 
Calculus
a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the yaxis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 … 
Calculus
Use the disk method to find the volume of the solid generated when the region bounded by y=15sinx and y=0, for 0 </= x </= pi, is revolved about the xaxis. 
Calculus (Solid of Revolution)
The region R is bounded by the xaxis, x = 1, x = 3, and y = 1/x^3. C. Find the volume of the solid generated when R is revolved about the xaxis. 
calculus
sketch the region R bounded by the graphs of the equations, and find the volume of the solid generated if R is revolved about the x axis when y=x^2 y=4x^2 
CALCULUS HELP PLZ
The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the xaxis. C. The solid formed in part B is divided … 
CALCULUS
The region R is bounded by the xaxis, yaxis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the xaxis. C. The solid formed in part B is divided … 
calculus
the region bounded by the graph f(x)=x(2x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.