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Volume by integration problem

Bmanmcfly

Member
Mar 10, 2013
42
[solved]Volume by integration problem

I was just curious if I'm doing this wrong, but for the problem I am working on, I am rotating around the y axis a formula.

Part of the graph crosses into the negative x-axis.

So, my questions are; do I have to separate this into 2 integrals, one for the positive section and one for the negative section like is done with areas?

Also, if I do this split an there is a multiplier, do I keep this multiplier (in this case pi) on both halves? Or would that unintentionally create a 2pi?
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Since you cite $\pi$ as the multiplier, I assume you are using the disk method, and presumably the $x$-coordinate is the radius of the disks, which is squared, so you most likely may use one integral over the entire interval.

In the case of a split, you do want to apply the multiplier to both integrals, since:

\(\displaystyle k\int_a^b f(x)\,dx+k\int_b^c g(x)\,dx=k\left(\int_a^b f(x)\,dx+\int_b^c g(x)\,dx \right)\)
 

Bmanmcfly

Member
Mar 10, 2013
42
Since you cite $\pi$ as the multiplier, I assume you are using the disk method, and presumably the $x$-coordinate is the radius of the disks, which is squared, so you most likely may use one integral over the entire interval.

In the case of a split, you do want to apply the multiplier to both integrals, since:

\(\displaystyle k\int_a^b f(x)\,dx+k\int_b^c g(x)\,dx=k\left(\int_a^b f(x)\,dx+\int_b^c g(x)\,dx \right)\)
You were right on all counts...

I think I got the right answer, to check, with the disks I would put \(\displaystyle /int_{-3}^9\), or because it's y axis would I put \(\displaystyle /int^{-3}_9\)?

Since I seem to have the correct answer, I'm wagering it's the former.

Either way, how do you add [solved] to the title?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Yes, you want to use the smaller value for the lower limit and the larger value for the upper limit.

To mark a topic as solved, edit your first post, and there is a prefix box that you can select the [SOLVED] prefix.