Volume
posted by Jamie .
Find the volume of the solid generated by revolving the region bounded by the given curves and line about the yaxis.
y=50x^2
y=x^2
x=0

calculus 
bobpursley
as I see it, the upper and lower boundries cross at 5,25, os the integral will be from x=0 t0 5
so the dArea will be [(50x^2)x^2]dx
and you will rotate that about the y axis, so the volume will be INT 2PI*xdA or
int 2PI x(502x^2)dx
so integrate that. I will be happy to check it. 
Volume 
MathMate
Like all multiple integral problems, start with drawing a sketch of the bounding curves.
I have done that for you for this time, see:
http://img687.imageshack.us/img687/811/1342739949.png
If curves intersect, find the intersection points. In this case, it is at (5,25).
Then decide how you want to integrate, namely the order of integrating along x first, followed by y, or vice versa.
Using the ring method, and set up the double integral:
Volume
=∫∫2πx dy dx
y goes from x^2 to 50x^2 and
x goes from 0 to 5 (intersection point). 
Volume 
nana
2Pi(500/3)
Respond to this Question
Similar Questions

MATH
Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y  y3, x = 1, y = 1 (b) Revolved about the yaxis ? 
Volume of a solid  calculus
Find the volume of the solid generated by revolving the region bounded by the curves: y=2 Sqrt(x), y=4, x=0 about the xaxis 
Calculus
Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded by the curve y=x^2, below by the xaxis, and on the right by the line x=1, about the line x=2 
calculus
Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 the xaxis,the yaxis,and the line x = 4 
Math
Find the volume of the solid generated by revolving the following region about the given axis The region in the first quadrant bounded above by the curve y=x^2, below by the xaxis and on the right by the line x=1, about the line x=4 
calculus
Find the volume of the solid generated by revolving the region about the given line. The region in the second quadrant bounded above by the curve y = 16  x2, below by the xaxis, and on the right by the yaxis, about the line x = … 
Calculus
We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please? 
Calculus
I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 … 
Calculus
Can you please check to see if these answers are correct? 
Calculus
Use the disk method to find the volume of the solid generated by revolving about the yaxis the region bounded by the curves y=8−x^2 and the curve y=x^2.