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Integral problem

  1. Mar 24, 2008 #1
    [SOLVED] integral problem

    1. The problem statement, all variables and given/known data

    hi. my problems an integral which i cant solve. the integral is this-

    integral of [1-(e^(t/a))]^2 dt

    a is a constant. it came when i tried to find the total power through a LR circuit


    2. Relevant equations



    3. The attempt at a solution

    not sure at all.

    [1-(e^(t/a))]^3
    ----------------
    3 [ then???? ]
     
  2. jcsd
  3. Mar 24, 2008 #2
    This can be done with substitution:
    [tex]\int(1-{e}^{t/a})^{2}dt[/tex]
    Let [tex]u=t/a[/tex] and thus [tex]du=dt/a, dt={a}{du}[/tex].
    After expanding the integrand and putting [tex]a[/tex] (the constant) on the outside, it becomes:
    [tex]{a}\int{e}^{2u}-2e^u+1 du[/tex].
    Again, if you don't see it already, use substitution on the first part and manually do the other two easy parts.
    Let [tex]w=2u, dw=2du, \frac{1}{2}dw=du[/tex]
    [tex]\frac{1}{2}a\int{e^w}dw=\frac{1}{2}ae^w=\frac{1}{2}ae^{2u}=\frac{1}{2}ae^{2t/a}[/tex]
    The second part is easy:
    [tex]-a \int{2e^u}du=-2e^u=-2e^{t/a}[/tex]
    The third part is the easiest (I added the constant 'C' here):
    [tex]a \int du=au+C=a\frac{t}{a}+C=t+C[/tex] don't forget the substitution!
    Summing all of these gives these final answer:
    [tex]\int(1-{e}^{t/a})^{2}dt=\frac{1}{2}ae^{2t/a}-2e^{t/a}+t+C[/tex]
     
  4. Mar 25, 2008 #3
    hey thanks! a lot. how did you get the integral signs? (the big s) and the proper format?
     
  5. Mar 25, 2008 #4
    hey thanks! a lot. how did you get the integral signs? (the big s) and the proper format?
     
  6. Mar 25, 2008 #5
    [itex]\LaTeX[/itex] is what you're looking for go to

    https://www.physicsforums.com/showthread.php?t=8997

    [tex]\int_0^{\infty} e^{x^2}\;dx\rightarrow \int \mid e^{x^2}\mid \lim_{x\rightarrow\infty}=[/tex]

    [tex]\sum_{n=-\infty}^\infty \frac{x^n}{n!} = \lim_{n\rightarrow\infty} (1+x/n)^n[/tex]

    You can click on any bit of code and cut and paste it as well. Try these ones.
     
    Last edited: Mar 25, 2008
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