anonymous
  • anonymous
Find the volume of the solid formed by rotating the region bounded by: y=x^2+2 and y=x+8 around the line, x=4. Leave the answer in terms of pi.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
idk
anonymous
  • anonymous
lolz
yuki
  • yuki
so what you are basically doing is to find the volume of the washer (I usually call it a ring) and integrate it. what do you think the integrand is ?

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yuki
  • yuki
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yuki
  • yuki
if you see that the volume of each ring(washer) has a volume V = 2pi ( (4-sqrt(y-2))^2 - (4-(y-8))^2) dx so the integration will be\[2\pi \int\limits (4-\sqrt(y-2))^2- (4-(y-8))^2dx\]
yuki
  • yuki
oops, I meant dy
yuki
  • yuki
now all you have to do is to figure out the limit of integration
yuki
  • yuki
the bottom of the parabola starts at y = 2 and it ends at y = 11 so the limit of integration is from 2 to 11
yuki
  • yuki
once you integrate it you are done :)
yuki
  • yuki
If you would like, try using the shell method, which is also a good choice for this one :)

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