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Integral problem

[SOLVED] integral problem

1. Homework Statement

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. Homework Equations



3. The Attempt at a Solution

not sure at all.

[1-(e^(t/a))]^3
----------------
3 [ then???? ]
 

Answers and Replies

85
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]
 
hey thanks! a lot. how did you get the integral signs? (the big s) and the proper format?
 
hey thanks! a lot. how did you get the integral signs? (the big s) and the proper format?
 
hey thanks! a lot. how did you get the integral signs? (the big s) and the proper format?
[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:

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