Volume between two curves: f(x) = sin(pi*x) and g(x) = 2x^3 - 8x

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conalhughes

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f(x)=sin(pi*x) and g(x)=2x^3-8x. R is the region bounded by the two functions. what is the volume of R rotating around y=-4?
 
conalhughes said:
f(x)=sin(pi*x) and g(x)=2x^3-8x. R is the region bounded by the two functions. what is the volume of R rotating around y=-4?
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As this being a math help forum no helper here will solve this problem for you as that will not be helpful. Have you drawn a graph? Please graph these two functions showing where they intersect and post that diagram. If you can do a little more than just that, then please post that work. I assure you, that in the end it will be better if you solve your own problem with some friendly hints from helpers on this site.
 
conalhughes said:
f(x)=sin(pi*x) and g(x)=2x^3-8x. R is the region bounded by the two functions. what is the volume of R rotating around y=-4?
Click to expand...
If I were to solve this assignment:
  1. I would plot y= 2x^3-8x and y = sin(pi*x) and y = -4 (on same grid)

  2. I would determine points of intersections of these curves and lines - determine the range and the domain of the region of interest

  3. I would decide on method of integration of the volume of rotation ( washer method or disk method)

    and continue....

    Please show us what you have tried and exactly where you are stuck.

    Please follow the rules of posting in this forum, as enunciated at:

    READ BEFORE POSTING

    Please share your work/thoughts about this problem
 
It looks reasonable ... until you include the axis. What does it even mean to revolve around that?

1701636586591.png​

Maybe there's a typo? x=-4 wouldn't be too bad.
 
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