Author Topic: volume integration help (Read 590 times) Tweet Share

(Lu)^2 · « **on:** February 03, 2018, 05:59:03 pm »

Hey hey if someone could give me a hand with this text book question that would be much appreciated

"find the volume of the solid formed when the line x+3y-1=0 is rotated about the x-axis from x=0 to x=8"

RuiAce · « **Reply #1 on:** February 03, 2018, 06:07:44 pm »

Deleted a previous reply after realising something was amiss.
$\text{You need to sketch the graph of the line first.}\\ \text{When you do this, you realise that the graph}\\ \text{crosses over the }x\text{-axis at }x=1.$
$\text{So you must split the volume from 0 to 1, with that from 1 to 8.}$
$\text{Rearranging }x+3y-1=0\text{ gives }y = \frac13(1-x)\\ \text{and hence }\boxed{y^2 = \frac19(1-2x+x^2)}\\ \text{giving a volume integral of }\\\boxed{V = \pi \int_0^1 \frac19 (1-2x+x^2)\,dx + \pi \int_1^8 \frac19 (1-2x+x^2)\,dx}$

Search the forums now!

We have moved!

Author Topic: volume integration help (Read 590 times) Tweet Share

(Lu)^2

volume integration help

RuiAce

Re: volume integration help

Recent Posts

User:
Password: