Volumes of Solids of Revolutions Help!

  • Thread starter jzsc
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  • #1
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Homework Statement



Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

y=x, y=0, x=2, x=4; about x=1


The Attempt at a Solution


one of the radii is x=y but im not sure how to find the other one and the interval? Please explain this one to me. Thanks!
 

Answers and Replies

  • #2
SammyS
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Homework Statement



Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

y=x, y=0, x=2, x=4; about x=1

The Attempt at a Solution


one of the radii is x=y but I'm not sure how to find the other one and the interval? Please explain this one to me. Thanks!
Hello jzsc. Welcome to PF !

Which are you using, the disk method or the washer method ? Until you decide that, you can't specify a radius.
 
  • #3
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thank you SammyS! I am using the washer's method
 
  • #4
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[itex]2\Pi\int x f(x) dx[/itex]

The x is serving as the distance from the y-axis (the radius), so if you're rotating around x=1 rather than x=0....

(I don't know how to put the a & b above and below the integrand)
 
Last edited:
  • #5
ehild
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[itex]2\Pi\int x f(x) dx[/itex]

(I don't know how to put the a & b above and below the integrand)

[itex]2\Pi\int_a^b x f(x) dx[/itex]

ehild
 

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