Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

is that my A?

Answer 5

Yes

Answer 6

oh i got 2/ sqrt(2)-1

Answer 7

but how do you do the integrarion by parts?

Answer 8

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.

Answer 9

Next we have to find the x and y coordinate.

Answer 10

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