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# Integration by Parts [SOLVED]

Registered User regular
edited December 2009
Ugh. I don't even remember if this was in Calc I or II.

Anyway, I'm integrating exp(-Dt)dt. If I set u=exp(-D), v=exp(t), I get exp(-Dt). If I set u=1, x=exp(-Dt), I get -1/D*exp(-Dt). Those are not the same. Why aren't they the same?

Oh, good luck, ceres!

Steam: Autumn_Thunder - SC2: AutumnThundr.563 (NA) - Hearthstone: AutumnThundr.1383

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When the last moon is cast over the last star of morning And the future has past without even a last desperate warningRegistered User, Moderator mod
edited December 2009
It's Calc I. I have it now. The final is next week. Please kill me.

ceres on
And it seems like all is dying, and would leave the world to mourn
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Nah Registered User regular
edited December 2009
so you're integrating e^(-Dt) dt or e^(-Dt) dD?

also, this might help

Usagi on
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Registered User regular
edited December 2009
Oh, sorry. The differential term is dt. I'm pretty sure the correct answer is the second one but I can't figure out why the first one doesn't work.

SkyEye on
Steam: Autumn_Thunder - SC2: AutumnThundr.563 (NA) - Hearthstone: AutumnThundr.1383

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Nah Registered User regular
edited December 2009
ok, so you're integrating e^(-Dt) dt where D is a constant

why are you integrating by parts?

Usagi on
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Registered User regular
edited December 2009
Hey, just wondering - if:

u = exp(-D)
v = exp(t)

Then

uv = exp(-D) * exp(t) = exp(-D + t) =/= exp(-Dt)

?

ecco the dolphin on
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Registered User regular
edited December 2009
SkyEye wrote: »
Ugh. I don't even remember if this was in Calc I or II.

Anyway, I'm integrating exp(-Dt)dt. If I set u=exp(-D), v=exp(t), I get exp(-Dt). If I set u=1, x=exp(-Dt), I get -1/D*exp(-Dt). Those are not the same. Why aren't they the same?

The product of exp(-D) and exp(t) is exp(-D + t).

EDIT: Oops, eeccccoo beat me to it. Guess I should actually read the other replies before making my own :P

Clipse on
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Registered User regular
edited December 2009
Goddamn, I knew this would make me look stupid somehow.

SkyEye on
Steam: Autumn_Thunder - SC2: AutumnThundr.563 (NA) - Hearthstone: AutumnThundr.1383

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Registered User regular
edited December 2009
SkyEye wrote: »
Goddamn, I knew this would make me look stupid somehow.

Nah, don't fuss.

You're not the first person to have made this mistake.

Besides, now that you've made the mistake publicly, you'll remember when it comes to your exam!

ecco the dolphin on