Volumes last week of calc

1. May 28, 2008

physicsed

[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

$$\int^{1}_{2} \pi \frac{1}{x} dx$$

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

2. May 28, 2008

Dick

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. May 28, 2008

physicsed

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

if you help me with this problem, i am sure i will get the rest of the problems.

4. May 28, 2008

Dick

It's a power law integral. Like x^n. What's n in this case? What's the antiderivative?

5. May 28, 2008

physicsed

$$\pi \int^{2}_{1} \frac{1}{x^2} dx$$

Last edited: May 28, 2008
6. May 28, 2008

Dick

Fine start. Now what's the antiderivative of 1/x^2?

7. May 28, 2008

physicsed

$$\pi [ \frac{x^{-3}}{-3}]$$

8. May 28, 2008

Dick

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: May 28, 2008
9. May 28, 2008

physicsed

since it's divided by 1, isn't it negative n
=x^-2

10. May 28, 2008

Dick

Yes, it is. Can you fix your antiderivative?

11. May 28, 2008

physicsed

(-1/3)x^-3

12. May 28, 2008

Dick

Beep. Beep. Beep. You goofed it again. What's -2+1? Think this time.

13. May 28, 2008

physicsed

righttt

pi [(1/-1)x^-1]

14. May 28, 2008

Dick

Much better! You've got it now, right? And you promised that meant you could get all the others.

15. May 28, 2008

thanks buddy