anonymous
  • anonymous
i'm trying to find the centroid of the region bonded by the given curves y= sinx; y=cosx, x=o and x=pi/4
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
The first thing you need is the mass so if we set f(x) = sin(x) and g(x) = cos(x) to get the mass we want: \[\int\limits_{0}^{π/4}[\cos(x)-\sin(x)]dx\]
anonymous
  • anonymous
i know thats part i think im getting the wrong numbers when i plug the integral
anonymous
  • anonymous
This integral should be equal to √(2) -1

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anonymous
  • anonymous
is that my A?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
oh i got 2/ sqrt(2)-1
anonymous
  • anonymous
but how do you do the integrarion by parts?
anonymous
  • anonymous
This first integral isn't by parts. ∫cos(x)dx = sin(x) ∫sin(x)dx = -cos(x) sin(x)+cos(x) evaluated from 0 to π/4. At π/4 we get √2 and at 0 we get 1.
anonymous
  • anonymous
Next we have to find the x and y coordinate.
anonymous
  • anonymous
For the x coordinate take: \[\int\limits_{0}^{π/4}x[\cos(x)-\sin(x)]dx\] and divide by √2 - 1 and the y coordinate take: \[\int\limits\limits_{0}^{π/4}(1/2)[\cos ^{2}(x) - \sin ^{2}(x)]dx\] and divide that by √2 - 1

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