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Simply then integrate

  • Thread starter 7yler
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  • #1
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I am familiar with integration, but I'm stumped with this. How do you integrate something such as [tex]\int[/tex](from 0 to 2)[tex]\sqrt{65e(to the power of 2t}[/tex]dt

That is supposed to be the square root of 65e to the power of 2t.
 

Answers and Replies

  • #2
1,254
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you should simplify the argument first.
 
  • #3
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Here's how you'd write your integral using LaTeX:
Code:
\int_0^2 \sqrt{65 e^{2t}} dt
which, when enclosed by "TEX" and "/TEX" (with the quotation marks replaced by square brackets), gives
[tex]\int_0^2 \sqrt{65 e^{2t}} dt[/tex]​

Anyway, try using the fact that [itex]\sqrt{a}=a^{1/2}[/itex].
 
  • #4
dextercioby
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Well, another to put it would be to see that

[tex] e^{2t} = (e^t)^2 [/tex]

which would fit nicely with the square root.
 
  • #5
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So I would get 65e^2 - 65?
 
  • #6
dextercioby
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Well, the 65 is still under a radical. Only e^t is squared under the square root.
 
Last edited:
  • #7
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So 65(e^2) - 65 is what I get when I follow through with the calculations, but I'm told that that answer is incorrect.
 
  • #8
dextercioby
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You didn't understand. The 65 must be under the radical sign, as in [itex] \sqrt{65} [/itex].
 
  • #9
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Oh okay. Thank you very much.
 

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