## anonymous 5 years ago 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

1. 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: $\int\limits_{0}^{π/4}[\cos(x)-\sin(x)]dx$

2. anonymous

i know thats part i think im getting the wrong numbers when i plug the integral

3. anonymous

This integral should be equal to √(2) -1

4. anonymous

is that my A?

5. anonymous

Yes

6. anonymous

oh i got 2/ sqrt(2)-1

7. anonymous

but how do you do the integrarion by parts?

8. 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.

9. anonymous

Next we have to find the x and y coordinate.

10. 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