anonymous
  • anonymous
Another integral problem!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
anonymous
  • anonymous
So I know that the integral is -cos^3 (x) / 3 + c for the integral of cos^2 (x) * sin(x)
anonymous
  • anonymous
So the first part would be zero because 2/3 - 2/3 is 0

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anonymous
  • anonymous
I mean 1/3 - 1/3
anonymous
  • anonymous
But what about the second part? Wouldn't that just be adding 1/3 and 1/3 together to get 2/3?
ganeshie8
  • ganeshie8
For the second part, you need to honor the absolute bars, for what values of `x`, is the expression `cos^2x*sinx` negative ?
anonymous
  • anonymous
When x is pi/2 to 3pi/2
ganeshie8
  • ganeshie8
|dw:1436014008840:dw|
anonymous
  • anonymous
Oh wait I read it wrong
anonymous
  • anonymous
OH okay.
ganeshie8
  • ganeshie8
so simply evaluate the integral between (0, pi) and multiply by 2
anonymous
  • anonymous
Ohhh which is 4/3!!
ganeshie8
  • ganeshie8
yes!
anonymous
  • anonymous
And then for the last part we just multiply 4/3 by 30~
ganeshie8
  • ganeshie8
Excelent!
anonymous
  • anonymous
^however how does this work? just multiplying it by 30...
anonymous
  • anonymous
Because I don't think you would be able to do that in a another integral about has bounds...
ganeshie8
  • ganeshie8
you must be knowing that definite integral can be interpreted as "signed area under the curve" ?
anonymous
  • anonymous
Ohhhhh yeah.
ganeshie8
  • ganeshie8
Look at the graph, it clearly repeats every 2pi, yes ?
anonymous
  • anonymous
yeah.... it's summer.... thank you!
ganeshie8
  • ganeshie8
np :)

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