Chapter 14 - Multiple Integrals - 14.3 Double Integrals In Polar Coordinates - Exercises Set 14.3 - Page 1025: 37

False

Per Theorem $14.3,3,$ the volume of a double integral is evaluated as \[ \int_{\alpha}^{\beta} \int_{r_{1}(\theta)}^{r_{2}(\theta)} r \mathrm{d} r \mathrm{d} \theta \] The $\mathbf{r}$ is next to $\mathrm{d} r .$ The question's double integral doesn't contain the needed extra $r,$ so it's incorrect.