# Thread: Volume & Improper Integrals

1. ## Volume & Improper Integrals

Hi, I had a two part question:

We just learned improper integrals today and I am finding the concept a little tricky. (Quite frankly, I suck at limits in general).

However, I am stuck as to when we are finding the volume

Would the volume not be $\frac{\ln(0.7x+1.7)}{0.7}$ from 0 to infinity?

And when I tried doing:
$\frac{\ln(0.7\infty+1.7)}{0.7} - \frac{\ln(0.7(0)+1.7)}{0.7}$
you would get infinity minus whatever number on the right?

I am so confused. I cannot find a good example online, in my books or in my notes.

2. The volume is...

$V= \pi\cdot \int_{0}^{\infty} \frac{dx}{(.7 x +1.7)^{2}}$ (1)

... so that it is finite, even if the area...

$R= \int_{0}^{\infty}\frac{dx}{.7 x + 1.7}$ (2)

... is infinite... a little nice 'paradox' ...

Kind regards

$\chi$ $\sigma$