Chapter 9 - Further Applications of the Integral and Taylor Polynomials - 9.3 Center of Mass - Exercises - Page 483: 21

$(\frac{9}{20}, \frac{9}{20})$

$M_{x}$ = $\frac{1}{2}\int_0^1{(x-x^{4})}dx$ = $\frac{3}{20}$ $M_{y}$ = $\int_0^1{x(\sqrt x-x^{2})}dx$ = $\frac{3}{20}$ $A$ = $\int_0^1{(\sqrt x-x^{2})}dx$ = $\frac{1}{3}$ so the coordinates of the centroid are $(\frac{9}{20}, \frac{9}{20})$