Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.3 Center of Mass - Exercises - Page 483: 25

$(\frac{\pi{\sqrt 2-4}}{4(\sqrt 2-1)}, \frac{1}{4(\sqrt 2-1)})$

$M_{x}$ = $\frac{1}{2}\int_0^{\frac{\pi}{4}}(cos^{2}x-sin^{2}x)dx$ = $\frac{1}{4}$ $M_{y}$ = $\int_0^{\frac{\pi}{4}}x(cosx-sinx)dx$ = $\frac{\pi{\sqrt 2}}{4}-1$ $A$ = $\int_0^{\frac{\pi}{4}}(cosx-sinx)dx$ = $\sqrt 2-1$ so the coordinates of the centroid are $(\frac{\pi{\sqrt 2-4}}{4(\sqrt 2-1)}, \frac{1}{4(\sqrt 2-1)})$