1
$\begingroup$

I'm fairly okay with volumes of revolutions in general but what if I have to rotate it about 2 curves?

The question here asks:

"The region bounded by the given curves is rotated about a specific axis. Set up, but do not evaluate, an integral which gives the volume of the resulting solid by any method."

$y=4x-x^2$,$y=8x-2x^2$ about $x=-2$ and then about $y=-5$

If this asked me how to rotate about the line $x=-2$, that would be fine. How about if I am asked to rotate the curve about $x=-2$ and then $y=-5$? How would I go about doing that?

$\endgroup$
1
$\begingroup$

The wording is confusing, but I'm pretty sure it's simply two separate questions. In other words, they are not asking you to create a solid as the result of rotating over two axes one after another. Think of this as two separate questions:

  1. rotate the given region about the axis $x=-2$;

  2. rotate the given region about the axis $y=-5$.

$\endgroup$
  • $\begingroup$ That's super misleading but yeah makes sense. Thanks! $\endgroup$ – Future Math person Feb 14 '17 at 19:59
0
$\begingroup$

With these problems, I always find drawing a graph of both functions to be helpful. Rotating about a $y=$ line, you use the washer method with the given functions. Rotating about a $x=$ line, you will need to change the equations to functions of $y$ rather than $x$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.