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Math Help - Improper Integral

  1. #1
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    Improper Integral

    1. Determine whether the improper integral converges or diverges.

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  2. #2
    No one in Particular VonNemo19's Avatar
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    Where are you stuck?
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  3. #3
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    Well , I first let u=x-2, so du=dx. Also, when x=22, u=20, and when x=20,u=18.

    In another question exactly the same just different numbers, i did my own procedure and it worked out, but for this one, im not sure if I have to split up the integral into two parts since last time the denominator of the integral u approached 0 (unbounded near u=0).
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    anyone know how to solve this?
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  5. #5
    No one in Particular VonNemo19's Avatar
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    Note that



    |x-21|=\left\{\begin{array}{cc}-(x-21),&\mbox{ if }<br />
x\leq 21\\x-21, & \mbox{ if } x>21\end{array}\right.

    See where I'm goin here? You've gotta break it up.
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  6. #6
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    yeah, i understand that, but im not sure what are the upper and lower bounds of the integral with a negative sign since x less than or equal to 21.
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  7. #7
    No one in Particular VonNemo19's Avatar
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    = \lim_{x\to{21}^-}\int_{20}^{21}\frac{1}{\sqrt[3]{-(x-21)}}dx+\lim_{x\to21^+}\int_{21}^{22}\frac{1}{\sqr  t[3]{x-21}}
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  8. #8
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    does it converge to 3? This is what i got as an answer.
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  9. #9
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    Anyone?
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