Volume of solid rotating y=x² between x=2 and x=4 about x=7

[willson.slp]

I'm have trouble with a homework problem having to do with find volume of an area. the problem reads:

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=x^2 , y=0 , x=2 , x=4;


about the line x=7

I've tried using the washer method and also the shell method with no luck. Any help would be greatly appreciated.

Thanks

 

[ehild]

Show your attempt, please, so as we can find out what went wrong.

ehild

 

[willson.slp]

since its rotating about the line x=7, I solved for y first

Im using pi*intergral from 0 to 16 of ((7-sqrt(y))^2-(7-5)^2)dy

I think I'm messing up with what my inner and outer radius' are and possibly the bounds

 

[ehild]

Y goes from 0 to x^2. First I would get the volume of a cylindrical shell of radius 7-x, thickness dx and height y=x^2. Then the integration with respect to x goes from x=2 to x=4.

ehild

 

[willson.slp]

That did it!
I came up with 424pi/3

When I initially tried the shell method I was using just x for the radius instead of 7-x. Thanks again for the help!

 

[ehild]

Is not it 436pi/3?

ehild

 

[willson.slp]

I double checked it and still got 424pi/3
The homework is online and I got it correct