# technical calculus problem

• Jan 22nd 2009, 02:16 PM
patrickg
technical calculus problem
I hate that my first post on this forum is a question!! These are two questions I can not figure out:

1. Find the volume of the solid of revolution obtained by rotating R, defined by the bounds given in each exercise, about the y-axis.

Y^2=4X, 4X-3Y-4=0

2. Find the volume of the solid obtained by revolving the region bounded by y=square root of X , x=4

a. the x axis
b. the y axis
c the line x=5
d. the line y=3

I don't just need the answer, I need to understand what I need to do to get the answer. Thanks for any and all help.
• Jan 22nd 2009, 02:28 PM
Jhevon
Quote:

Originally Posted by patrickg
I hate that my first post on this forum is a question!! These are two questions I can not figure out:

1. Find the volume of the solid of revolution obtained by rotating R, defined by the bounds given in each exercise, about the y-axis.

Y^2=4X, 4X-3Y-4=0

did you graph the region? if not, do so.

then, turn your graph so that the positive x-axis is pointing up. do you see it now? we can use the disk (washer) method to find the volume. of course, we integrate with respect to y.

the volume is given by:

$V = \pi \int_a^b \Bigg[ \left( \frac 34y + 1 \right)^2 - \left( \frac {y^2}4 \right)^2 \Bigg]~dy$

$a$ and $b$ (with $b > a$) are the y-coordinates for the points of intersection of the two graphs--i leave them for you to find

(the shell method could work, but we would need two integrals, and that's too much trouble)

Quote:

2. Find the volume of the solid obtained by revolving the region bounded by y=square root of X , x=4

a. the x axis
b. the y axis
c the line x=5
d. the line y=3

I don't just need the answer, I need to understand what I need to do to get the answer. Thanks for any and all help.
you are missing one of the bounds with this problem. is it also bounded by the x-axis?