anonymous
  • anonymous
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) .
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
hey, how's it going?
anonymous
  • anonymous
hii, i am good
anonymous
  • anonymous
do you usually use this instead of group chat?

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anonymous
  • anonymous
yes
anonymous
  • anonymous
I see, so I dont really know which fundamental theorem its talking about... arent there 2 diff ones
anonymous
  • anonymous
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
anonymous
  • anonymous
O... is that the F(b)-F(a) one?
anonymous
  • anonymous
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?
anonymous
  • anonymous
not take the derivative
anonymous
  • anonymous
oh yeah, the integral xD
anonymous
  • anonymous
how do you take the integral of something like that...
anonymous
  • anonymous
factor out an x so you have ln((x)(x+2))
anonymous
  • anonymous
do you know how you can simplify it from there using a property of logs?
anonymous
  • anonymous
Ohhh, right. you can split it to lnx-ln(x+2)
anonymous
  • anonymous
not quite right, but almost
anonymous
  • anonymous
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
anonymous
  • anonymous
are you just supposed to memorize what the integral of lnx is
anonymous
  • anonymous
oh... i just looked it up and it turns into an integration by parts problem, so many different concepts! lol
anonymous
  • anonymous
i got it now, thanks!
anonymous
  • anonymous
ok, no problem

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