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Improper Integral

  1. Apr 1, 2004 #1
    How do I do
    [tex] \int_{3}^{6} (5-x)^{\frac{-1}{3}} \,dx [/tex]
    ?

    I also need to know how to do
    [tex] \lim_{t\rightarrow\infty} \int_{-t}^{t} \frac{x}{x^2 + 1} \,dx [/tex]
     
    Last edited: Apr 1, 2004
  2. jcsd
  3. Apr 1, 2004 #2

    ahrkron

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    Staff Emeritus
    Gold Member

    You could do both by substitution. Try the second one first. Define
    [tex]u=x^2+1[/tex].
    What is [tex]du[/tex]?

    However, there is a hidden trick on the second one... draw the integrand as a function of x... can you tell its area from -t to t "by eye"?
     
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