What's Next in Calculus: Solving Volumes with Integrals

[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 what's next. can anyone inform me, please

 

[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.

 

[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.

 

[Dick]

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

 

[physicsed]

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

 

[Dick]

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

 

[physicsed]

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

 

[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'.

 

[physicsed]

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

 

[Dick]

Yes, it is. Can you fix your antiderivative?

 

[physicsed]

(-1/3)x^-3

 

[Dick]

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

 

[physicsed]

righttt

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

 

[Dick]

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.

 

[physicsed]

thanks buddy

your awesome

 

[Dick]

It's "you're awesome". I'm correcting grammar tonight. Thanks.