More integration using cylindrical shells

Sep 2009
26
0
The region bounded by the given curves is rotated about the y-axis.

Find the volume V of the resulting solid by any method.

Using cylindrical shells,
2pi*(the integral from 0 to 4) of (x-2)(((-x^2)+6x-8)-0)

I'm pretty sure this is wrong because the answer I get, -64pi/3 makes no sense. Any help is appreciated.

Thanks,
Jay
 

skeeter

MHF Helper
Jun 2008
16,217
6,765
North Texas
The region bounded by the given curves is rotated about the y-axis.

Find the volume V of the resulting solid by any method.

Using cylindrical shells,
2pi*(the integral from 0 to 4) of (x-2)(((-x^2)+6x-8)-0)

I'm pretty sure this is wrong because the answer I get, -64pi/3 makes no sense. Any help is appreciated.

Thanks,
Jay
do you make a sketch of the graph before setting up the integral?

reason I ask ...

your limits of integration are incorrect, should be 2 to 4

the radius of revolution is x , not (x-2)
 

VonNemo19

MHF Hall of Honor
Apr 2009
1,849
540
Detroit, MI
The region bounded by the given curves is rotated about the y-axis.

Find the volume V of the resulting solid by any method.

Using cylindrical shells,
2pi*(the integral from 0 to 4) of (x-2)(((-x^2)+6x-8)-0)

I'm pretty sure this is wrong because the answer I get, -64pi/3 makes no sense. Any help is appreciated.

Thanks,
Jay

Factoring \(\displaystyle -(x-4)(x-2)\Rightarrow{\text{ zeros at }}x=2,4\).

So, why do you go from 0 to 4?