Question

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.

Answer 1

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

Answer 2

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

Answer 3

yea glad your still on and yes i will

Answer 4

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

Answer 5

just pi* the function squared

Answer 6

okay so do you have a graphing calculater

Answer 7

negative on that prolly should have one being in calc

Answer 8

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)

Answer 9

do you have a mac

Answer 10

nope one sec

Answer 11

I got x=1

Answer 12

sec

Answer 13

what did you intergrate

Answer 14

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

Answer 15

ooh okay. yeah you get 1 and -2

Answer 16

so those are your domain of integration

Answer 17

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

Answer 18

cuz I got a wierd fraction

Answer 19

no it's from a worksheet

Answer 20

this is very hard without being able to draw a graph

Answer 21

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---

Answer 22

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

Answer 23

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

Answer 24

thats the volume formula

Answer 25

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)

Answer 26

ok thank you very much for your help

Answer 27

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