Volume of a graph (Washer)

Question

masterchief · Answer

Find the volume of $$y=\sqrt{x}$$ about x=4

masterchief · Answer

I started with $$x=y^2$$ so would that be the outer radius?

solomonzelman · Answer

|dw:1441595115874:dw|roughly

solomonzelman · Answer

x=y² is not the same as y=√x
because it will have a twice larger volume

masterchief · Answer

I'm sorry I forgot to mention it is bounded by y=0 so just quadrant 1

solomonzelman · Answer

oh, and then if it is rotated about x=4, then I will assume that this is where the √x region ends at?

masterchief · Answer

Yes

solomonzelman · Answer

Oh, ok, so you know that your limits of integration are from 0 to 2.

$\large\color{black}{ \displaystyle \int_{0}^{2} \pi\left(y^2\right)dy }$

solomonzelman · Answer

So, you can tell that your radius is y², and it is from y=0 to y=2.
THis is what I would do.

solomonzelman · Answer

I missed it should e y^4

solomonzelman · Answer

$\large\color{black}{ \displaystyle \int_{0}^{2} \pi\left(y^2\right)^2dy }$

because radius squared.
Sorry

solomonzelman · Answer

So that is just an integral of $\pi$y$^4$ from y=0 to y=2.

masterchief · Answer

Wow I tried this the first time and I guess I integrated incorrectly so I was so confused!

masterchief · Answer

Thank you

solomonzelman · Answer

you can put integral into wolfram.
what is important is to get a good practice of making a setup of the integral for volume.

integration you know already....

masterchief · Answer

Absolutely

solomonzelman · Answer

32π/5 is what i got.

(want to know how to make a π • ÷ × √ with no latex?)

masterchief · Answer

Sure!

danjs · Answer

here are some probs with the solns,    pg3 has a nice little summary

masterchief · Answer

That will definitely be useful, thank you

solomonzelman · Answer

I am glitching a bit