anonymous
  • anonymous
find the volume of the solid using shell method, region of y=sqrt2, x=y^2 , x=0. about the x-axis
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Ok which function is on top?
anonymous
  • anonymous
y=sqrt2, bounded on left by y -axis and below by x=y^2
anonymous
  • anonymous
just confirming it is y=\[y=\sqrt(2)\] x= x^2 right functions?

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anonymous
  • anonymous
-- correction x=y^2
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok so x=y^2 is a side way parabola facing in the positive x direction(right) y=sqrt(2) is just a horizonal striaght line We need to find intersection of of lines
anonymous
  • anonymous
y=sqrt2 right?
anonymous
  • anonymous
The intersection point will have y=sqrt(2)
anonymous
  • anonymous
when x = 2
anonymous
  • anonymous
what is x intersection is 2
anonymous
  • anonymous
so (2,sqrt(2)
anonymous
  • anonymous
good so far?
anonymous
  • anonymous
yes
anonymous
  • anonymous
So the region we are rotating has these points(0,0)-- origin (0,sqrt(2)top left corner, (2,sqrt(2) intersection
anonymous
  • anonymous
any questions?
anonymous
  • anonymous
so far good, i have a drawing set up
anonymous
  • anonymous
So we are going to use shell method which is just add up bunch off cylinder
anonymous
  • anonymous
Volume of cylinder is pi*radius^2*h
anonymous
  • anonymous
got ya
anonymous
  • anonymous
So if you look your drawing(may be draw horizonal rectangle) you will see that the y value of function represent radius
anonymous
  • anonymous
and the function x=y^2 represent h
anonymous
  • anonymous
yea from the integral of 0 to sqrt2 right?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
\[2\pi\int\limits(y*y^2 dy(\]
anonymous
  • anonymous
you got the limit of the integration right
anonymous
  • anonymous
so just integrate that? with the height as y^2?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
oooh thank you, i kept thinking of subtracting sqrt2 from the height wasn't really paying attention that this was respect to y. Thank you for all your help:)

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