The region bounded by the curve, y=x^2+1, and the line, y=-x+3, is rotated around the x-axis to generate a solid. Find the volume of the solid.

- anonymous

- schrodinger

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- anonymous

hey I saw you post this question earlier but you logged off

- anonymous

I'm gunna try and solve it will you be on?

- anonymous

yea glad your still on and yes i will

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## More answers

- anonymous

do you have the Volume equation? or is it just pi*the function squared

- anonymous

just pi* the function squared

- anonymous

okay so do you have a graphing calculater

- anonymous

negative on that prolly should have one being in calc

- anonymous

its fine. You could use the calculater to see where these functions intersect. Without one, just set the equations equal to eachother and solve (do this and tell me what you get)

- anonymous

do you have a mac

- anonymous

nope one sec

- anonymous

I got x=1

- anonymous

sec

- anonymous

what did you intergrate

- anonymous

I didn't I set them to each other and solved algebra

- anonymous

ooh okay. yeah you get 1 and -2

- anonymous

so those are your domain of integration

- anonymous

do you have a final answer (from the book or something)

- anonymous

cuz I got a wierd fraction

- anonymous

no it's from a worksheet

- anonymous

this is very hard without being able to draw a graph

- anonymous

http://www.wolframalpha.com/input/?i=integrate&a=*C.integrate-_*Calculator.dflt-&f2=pi%28-x%2B3%29^2-pi%28x^2%2B1%29^2&f=Integral.integrand_pi%28-x%2B3%29^2-pi%28x^2%2B1%29^2&f3=-2&f=Integral.rangestart_-2&f4=1&f=Integral.rangeend_1&a=*FVarOpt.1-_**-.***Integral.variable---.**Integral.rangestart-.*Integral.rangeend---

- anonymous

that shows you what I set up for my integral. Its hard to explain via chat but try this:
pi*(outter radius)^2 - pi*(inner radius)^2

- anonymous

alright thanx but why did u square each equation? how did u know to do that?

- anonymous

thats the volume formula

- anonymous

because when you rotate the shape around the x-axis its 3-dimensional. and you subtract the inner radius because thats the hole the shape makes when you rotate it. (so the shape looks like a doughnut)

- anonymous

ok thank you very much for your help

- anonymous

you are welcome let me know if you have any others.....get a graphing calc

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