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Volumes last week of calc

  • Thread starter physicsed
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  • #1
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[SOLVED] volumes... last week of calc

i was absent when we went over the volume section.

y= 1/x, x= 1, x= 2, y= 0,; about the x-axis

[tex]
\int^{1}_{2} \pi \frac{1}{x} dx
[/tex]

i don't know whats next. can anyone inform me, please
 

Answers and Replies

  • #2
Dick
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You could actually do the integration, but that would be wrong because you haven't set it up right either. You integrate pi*r^2 where r is the radius of the disk over the volume. I'd suggest checking a few examples in your textbook.
 
  • #3
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[tex]\int^{1}_{2} \pi [\frac{1}{x}]^2 dx[/tex]

if you help me with this problem, i am sure i will get the rest of the problems.
 
  • #4
Dick
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It's a power law integral. Like x^n. What's n in this case? What's the antiderivative?
 
  • #5
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[tex] \pi \int^{2}_{1} \frac{1}{x^2} dx[/tex]
 
Last edited:
  • #6
Dick
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Fine start. Now what's the antiderivative of 1/x^2?
 
  • #7
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[tex] \pi [ \frac{x^{-3}}{-3}] [/tex]
 
  • #8
Dick
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Beep. Wrong. The antiderivative of x^n is x^(n+1)/(n+1). What's n in this case? Unless that's a careless error because you are paying more attention to texing than thinking, you may have missed more than 'volumes'.
 
Last edited:
  • #9
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since it's divided by 1, isn't it negative n
=x^-2
 
  • #10
Dick
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Yes, it is. Can you fix your antiderivative?
 
  • #11
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(-1/3)x^-3
 
  • #12
Dick
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Beep. Beep. Beep. You goofed it again. What's -2+1? Think this time.
 
  • #13
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righttt

pi [(1/-1)x^-1]
 
  • #14
Dick
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righttt

pi [(1/-1)x^-1]
Much better! You've got it now, right? And you promised that meant you could get all the others.
 
  • #15
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thanks buddy

your awesome
 
  • #16
Dick
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It's "you're awesome". I'm correcting grammar tonight. Thanks.
 

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