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Math Help - Volume & Improper Integrals

  1. #1
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    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.
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  2. #2
    MHF Contributor chisigma's Avatar
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    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
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