# Volumes last week of calc

[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

Related Calculus and Beyond Homework Help News on Phys.org
Dick
Homework Helper
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.

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

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

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

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

Last edited:
Dick
Homework Helper
Fine start. Now what's the antiderivative of 1/x^2?

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

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

Dick
Homework Helper
Yes, it is. Can you fix your antiderivative?

(-1/3)x^-3

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

righttt

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

Dick
Homework Helper
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.

thanks buddy