Find the mass of a rod of length 2m with density $\delta$(x) = $\sqrt{2x}$ kg/m given at a distance of x m from the left end. I have that mass is equal to $\int_0^2\delta(x)dx$, which when I substitute in the value for $\delta(x)$, I get $8/3$ kg, but the solutions for this problem show that the answer is $2\sqrt6$ kg. Am I missing something?

Notice, there is some error in your calculation, $$\int_{0}^{2}\delta (x)\ dx=\int_{0}^{2}\sqrt {2 x}\ dx=\sqrt 2\int_{0}^{2} \sqrt x\ dx=\sqrt 2\left[\frac{x^{3/2}}{3/2}\right]_{0}^{2}=\sqrt 2\left[\frac{2^{3/2}}{3/2}-0\right]=\frac{2\cdot 2\sqrt 2}{3}=\color{red}{\frac{8}{3} \ kg}$$
