Quick intergration question

b0bd0db0bd0d Registered User regular
edited July 2008 in Help / Advice Forum
I'm having some trouble intergrating this:
X^3 (1+x^2)^(1/2)

Picture(view it alone to see it correctly):

f_MSP22437868m_0df8f83.gif

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

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Posts

  • ecco the dolphinecco the dolphin 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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  • Folken FanelFolken Fanel 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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  • Folken FanelFolken Fanel anime af When's KoFRegistered User regular
    edited June 2008
    Fuck it I was bored so here you go. Answer in spoiler:
    PAForumsReplyCopy.gif

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  • b0bd0db0bd0d 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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  • Folken FanelFolken Fanel 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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  • ecco the dolphinecco the dolphin 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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  • Folken FanelFolken Fanel 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.

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  • ecco the dolphinecco the dolphin 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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  • Folken FanelFolken Fanel 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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  • FallingmanFallingman Registered User regular
    edited June 2008
    I read this as "quick interrogation question"

    I am SO disappointed.

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  • b0bd0db0bd0d Registered User regular
    edited June 2008
    well, don't just stand there. Interrogate man!

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  • Simon MoonSimon Moon 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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  • ecco the dolphinecco the dolphin 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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    Penny Arcade Developers at PADev.net.
  • Folken FanelFolken Fanel 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....

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