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anonymous

  • 5 years ago

1. Consider y' = ln(2x + x^2) ; y(1) = ln 9 . a) Using the fundamental theorem of calculus, solve the differential equation. Then find y(3) .

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  1. anonymous
    • 5 years ago
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    hey, how's it going?

  2. anonymous
    • 5 years ago
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    hii, i am good

  3. anonymous
    • 5 years ago
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    do you usually use this instead of group chat?

  4. anonymous
    • 5 years ago
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    yes

  5. anonymous
    • 5 years ago
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    I see, so I dont really know which fundamental theorem its talking about... arent there 2 diff ones

  6. anonymous
    • 5 years ago
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    the fundamental theorem of calculus that it's referring to is basically that you can take the integral of a derivative of a function and get back the function

  7. anonymous
    • 5 years ago
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    O... is that the F(b)-F(a) one?

  8. anonymous
    • 5 years ago
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    oh wait, that means you just take the derivitave of ln(2x+x^2)... what does it mean "solve the differential equation"? solve for what?

  9. anonymous
    • 5 years ago
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    not take the derivative

  10. anonymous
    • 5 years ago
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    oh yeah, the integral xD

  11. anonymous
    • 5 years ago
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    how do you take the integral of something like that...

  12. anonymous
    • 5 years ago
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    factor out an x so you have ln((x)(x+2))

  13. anonymous
    • 5 years ago
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    do you know how you can simplify it from there using a property of logs?

  14. anonymous
    • 5 years ago
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    Ohhh, right. you can split it to lnx-ln(x+2)

  15. anonymous
    • 5 years ago
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    not quite right, but almost

  16. anonymous
    • 5 years ago
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    sorry, got kicked off the comp for a bit o_o. i meant lnx +ln(x+2), but im not sure you can take the integral of that

  17. anonymous
    • 5 years ago
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    are you just supposed to memorize what the integral of lnx is

  18. anonymous
    • 5 years ago
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    oh... i just looked it up and it turns into an integration by parts problem, so many different concepts! lol

  19. anonymous
    • 5 years ago
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    i got it now, thanks!

  20. anonymous
    • 5 years ago
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    ok, no problem

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