anonymous
  • anonymous
integration...
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
integrate x^2 sinx
Armor
  • Armor
This is a fairly lengthy problem to work out from scratch. You will have to apply integration by parts twice.
anonymous
  • anonymous
i just need the answer

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Armor
  • Armor
I won't just give you the answer. First, we need to identify the \(u,v\) for the first time. What do you think they should be?
anonymous
  • anonymous
i got -x^2 cosx + 2xsinx + 2cosx + C
anonymous
  • anonymous
wolfram puts it in a different form and isn't clear to me
Armor
  • Armor
Well, let's do it by hand then. What do you think the \(u,v\) should be?
anonymous
  • anonymous
yes
anonymous
  • anonymous
i used tabular method
anonymous
  • anonymous
so u was x^2... dv=sinx
Armor
  • Armor
Alright. Then \(du=2x\) and \(v=-\cos(x)\). So after one step of integration, we get\[-x^2\cos(x)-\int-\cos(x)2x dx=-x^2\cos(x)+2\int x\cos(x)dx\]Now we integrate by parts again.
Armor
  • Armor
This time with \(u=x\), and \(dv=\cos(x)\). We get\[-x^2\cos(x)+2\left(x\sin(x)-\int \sin(x)dx\right)\]Still following?
anonymous
  • anonymous
yes
Armor
  • Armor
Now we do that last integral and distribute the 2 to get \[-x^2\cos(x)+2x\sin(x)+2\cos(x)+C\]
anonymous
  • anonymous
ok, that's what i got!
Armor
  • Armor
Then you're right.
anonymous
  • anonymous
i couldn't tell that from just looking at wolf
anonymous
  • anonymous
but anyways, thank you!
Armor
  • Armor
You're welcome.

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