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\int r^{3}\mathrm{d}r
Evaluate the indefinite integral first.
\frac{r^{4}}{4}
Since \int r^{k}\mathrm{d}r=\frac{r^{k+1}}{k+1} for k\neq -1, replace \int r^{3}\mathrm{d}r with \frac{r^{4}}{4}.
\frac{4^{4}}{4}-\frac{0^{4}}{4}
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
64
Simplify.
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