# 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