$$ \sigma_\theta = \frac{1}{r^3} \int_0^r r'^2 \rho g dr' + \frac{1}{r^3} \int_0^R \frac{r'^2 \rho g R^3}{r'^3} dr' $$
Not quite. Current AI struggles with in specific coordinate bases. However, the perfect solution manual of the future will be interactive: Nonlinear Solid Mechanics Holzapfel Solution Manual
Many of the "problems" at the end of Holzapfel’s chapters are actually requests to derive specific identities or tensors mentioned in the text. The solutions are often "hidden in plain sight" within the chapter proofs. If you are stuck, re-trace the steps of the —this is where 90% of the mathematical difficulty lies. 2. Comparison with Computational Tools $$ \sigma_\theta = \frac{1}{r^3} \int_0^r r'^2 \rho g