anonymous
  • anonymous
How do you anti-derive x(2-x)^2?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
you have to take the integral
anonymous
  • anonymous
Would you mind showing me step by step?
anonymous
  • anonymous
I'm a little rough at this but I can try to help. I would go ahead and multiply through before calculating the integral. So you would have \[x(2-x)(2-x)\] then you would foil and multiply through by x. You end up with an integral that looks like this \[\int\limits 4x-4x ^{2}+x^3 dx\]

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anonymous
  • anonymous
Check my work... Like I said I'm a little rough at this. I believe you use a basic integration formula for each of those numbers...
anonymous
  • anonymous
correcto mundo
anonymous
  • anonymous
\[\int\limits 4x dx = 4(1/2)x ^{2}\]
anonymous
  • anonymous
You can make it much simpler by letting u=2-x and du=-1*dx. Then, you get -∫u^2*(2-u) du which expands to -∫2u^2-u^3 du = -[2u^3/3 - u^4/4] + c = -2(2-x)^2/3 + (2-x)^4/4 + c, if I'm not mistaken. MtHaleyGirl's solution is correct, but just seems like a lot more tedious multiplication than is necessary.
anonymous
  • anonymous
I DO take the long way... Scared of substitution but I just need a little practice. Good tip. Maybe it will make MY life easier.
anonymous
  • anonymous
Yesss, substitution makes life so much easier later on, once you get confident with it. It's an absolute must for a lot, if not all, of advanced techniques of integration.

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