Chapter 6 - Applications of the Integral - 6.2 Setting Up Integrals: Volume, Density, Average Value - Exercises - Page 298: 59

$c=\frac{3}{\sqrt[4] 5}$

$$f(c)=M$$ $$c^{4}=M$$ $$c^{4}=\frac{1}{3-0}\int_{0}^{3}x^{4}dx$$ $$c^{4}=\frac{1}{3}\int_{0}^{3}x^{4}dx$$ $$3c^{4}=\int_{0}^{3}x^{4}dx$$ $$3c^{4}=[\frac{x^{5}}{5}]_{0}^{3}$$ $$3c^{4}=\frac{3^{5}}{5}-\frac{0^{5}}{5}$$ $$3c^{4}=\frac{3^{5}}{5}$$ $$c^{4}=\frac{3^{4}}{5}$$ $$c=\frac{3}{\sqrt[4] 5}$$