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Hey guys I have a quick question.
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the specified axis. Sketch the region and a typical shell.
y=4x-x^2 , y=3 about x=1
For this question would i just sub in 3 into the y and just solve and find the interval. Then do the integration of 2pie x (4x-x^2) between the two intervals?
Your shells will extend from y = 0 , to y = 4x-x^2 . They will be too high.
The integrand should be f(x) - g(x).
You just have f(x).
that's all they gave me though, so how do i continue?
Hello, kashmoneyrecord3!
I don't understand your game plan,
but "just sub in 3" sounds like a bad idea . . .
Quote:
Use the method of cylindrical shells to find the volume generated by rotating
the region bounded by the given curves about the specified axis.
Sketch the region and a typical shell.
. .
Did you make a sketch?
Code:|
| : ..*..
| :.*:::::::*.
3+ *- - - - - -*
| *: :*
| : :
|* : : *
| : :
| : :
----*--+-----------+--*----
| 1 3 4
|
Formula: .
We have: .
Hence: .
how did you get the intervals?
Just the way you said in the Original Post, "just sub in 3 into the y".Quote:
Originally Posted by kashmoneyrecord3
Solve 3 = 4x-x^2 , for x. That should give x = 1, x = 3