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# Quick intergration question

Registered User regular
edited July 2008
I'm having some trouble intergrating this:
X^3 (1+x^2)^(1/2)

Picture(view it alone to see it correctly):

Any help? What would you use? Subsition? (u = X^2 + 1), (x^2 = u- 1)?

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Registered User regular
edited June 2008
I'd be tempted to use u^2 = x^2 + 1, myself. Or something similar.

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anime af When's KoFRegistered User regular
edited June 2008
Let x = tan(theta).
dx = sec^2(theta)d(theta)

Classic trig substitution problem.

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anime af When's KoFRegistered User regular
edited June 2008
Fuck it I was bored so here you go. Answer in spoiler:

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Registered User regular
edited June 2008
That's f'ing awesome. On a side note, you can use (u = X^2 + 1), (x^2 = u- 1) too. I was getting to step 10 and then was getting stuck. Kept thinking I wasn't getting the right answer because I wasn't simplifying all the way. Also, I can't order your stupid HP Lovecraft book if you don't have a shipping address.

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anime af When's KoFRegistered User regular
edited June 2008
I actually made a mistake. I forgot to include the square root on the left side of the first line. I edited my post above fixing my error.

As for your side note, I don't seem to get the same answer doing it that way, but at this hour I can't seem to see anything wrong with it necessarily.

I appreciate the offer, but no reimbursement is necessary on your end. The wish list is there as a remnant from the G&T Secret Santa.

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Registered User regular
edited June 2008
You know what's funny? Using the substitution u^2 = x^2 + 1 gets you straight to step 6 and lets you skip step 9. =P

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anime af When's KoFRegistered User regular
edited June 2008
eecc wrote: »
You know what's funny? Using the substitution u^2 = x^2 + 1 gets you straight to step 6 and lets you skip step 9. =P

Yeah, I definitely don't see this. Maybe it might simplify to the same answer at the end, but it definitely doesn't get you straight to step 6.

Folken Fanel on
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Registered User regular
edited June 2008
eecc wrote: »
You know what's funny? Using the substitution u^2 = x^2 + 1 gets you straight to step 6 and lets you skip step 9. =P

Yeah, I definitely don't see this. Maybe it might simplify to the same answer at the end, but it definitely doesn't get you straight to step 6.

u^2 = x^2 + 1
=> u du = x dx

x^3 * sqrt(x^2 + 1) dx = x^2 * sqrt(x ^2 + 1) * x dx = (u^2 - 1) * sqrt(u^2) * u du = (u^2 - 1) u^2 du = u^4 - u^2 du

Is step 6.

Edit: Whoops, hit step 7 by mistake. Went one too far.

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anime af When's KoFRegistered User regular
edited June 2008
Well hot damn, don't I feel silly.

Well done sir.

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Registered User regular
edited June 2008
I read this as "quick interrogation question"

I am SO disappointed.

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Registered User regular
edited June 2008
well, don't just stand there. Interrogate man!

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Registered User regular
edited July 2008
Hey, Folken, how'd you turn your TeX into a gif? I tried searching for dvi2gif, but didn't find anything useful...

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Registered User regular
edited July 2008
Simon Moon wrote: »
Hey, Folken, how'd you turn your TeX into a gif? I tried searching for dvi2gif, but didn't find anything useful...

You can always use ImageMagick's "convert" to change from postscript to gif, I believe.

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anime af When's KoFRegistered User regular
edited July 2008
Simon Moon wrote: »
Hey, Folken, how'd you turn your TeX into a gif? I tried searching for dvi2gif, but didn't find anything useful...

I'm using OS X to view the pdf in Preview and then just saving it as a GIF. But it would be fucking sweet if Ramius could code in LaTeX directly into the forums....

Folken Fanel on
Twitter: Folken_fgc Steam: folken_ XBL: flashg03 PSN: folken_PA SFV: folken_
Dyvim Tvar wrote: »
Characters I hate:

Everybody @Folken Fanel plays as.