Check my work:

What is the volume of the solid obtained by rotating the region bounded by the curves y = 1/x and the x-axis between x =1 and x =2 about the x-axis?

Question

Check my work:

 What is the volume of the solid obtained by rotating the region bounded by the curves y = 1/x and the x-axis between x =1 and x =2 about the x-axis?

anonymous · Answer

My work:$$\pi \int\limits_{2}^{1} (1/x)^2 -> 1/x^2 -> x ^{-2}$$
$$\pi \int\limits_{2}^{1} x ^{-2} = x ^{-1}.$$

anonymous · Answer

$$\pi[1/1 - 1/2] = \pi/2$$

nubeer · Answer

well yeah looks right.

phi · Answer

close, but you lost a minus sign.
I would use the limits  1 to 2  (not 2 to 1, which reverses the sign of the answer)

also,  the integral of x^(-2)  is -x^(-1)   
Test:  d/dx  - x^-1  =  +x^-2

anonymous · Answer

When I went from 1 to 2, I got -pi/2.  The textbook says the answer is pi/2.

phi · Answer

That is because you did not do the integral of x^-2 correctly
you should get
$$ -x^{-1} $$
not + x^-1

anonymous · Answer

yep, that's right!  I got the right answer now!  Thanks!