TestLaTex

[Thomas Klemm]

Use \tfrac instead of \dfrac in the \sqrt of the lower limit:

\( \dfrac{4}{3} \times \pi \times r^{3} - 2ab \sqrt{r^{2}- \left ( \dfrac{a}{2} \right ) ^2 - \left ( \dfrac{b}{2} \right ) ^2} - 8 \int_{\sqrt{r^{2} - \left ( \tfrac{a}{2} \right ) ^2 - \left ( \tfrac{b}{2} \right ) ^2}}^{r} \;\; \int_{0}^{\sqrt{r^2-y^2}} \sqrt{r^2-y^2-x^2} \;\; \mathrm{d}x \;\; \mathrm{d}y \)

---

Use [] instead of ():

\[ \dfrac{4}{3} \times \pi \times r^{3} - 2ab \sqrt{r^{2}- \left ( \dfrac{a}{2} \right ) ^2 - \left ( \dfrac{b}{2} \right ) ^2} - 8 \int_{\sqrt{r^{2} - \left ( \tfrac{a}{2} \right ) ^2 - \left ( \tfrac{b}{2} \right ) ^2}}^{r} \;\; \int_{0}^{\sqrt{r^2-y^2}} \sqrt{r^2-y^2-x^2} \;\; \mathrm{d}x \;\; \mathrm{d}y \]

---

Or then set \displaystyle explicitly:

\(\displaystyle \dfrac{4}{3} \times \pi \times r^{3} - 2ab \sqrt{r^{2}- \left ( \dfrac{a}{2} \right ) ^2 - \left ( \dfrac{b}{2} \right ) ^2} - 8 \int_{\sqrt{r^{2} - \left ( \tfrac{a}{2} \right ) ^2 - \left ( \tfrac{b}{2} \right ) ^2}}^{r} \;\; \int_{0}^{\sqrt{r^2-y^2}} \sqrt{r^2-y^2-x^2} \;\; \mathrm{d}x \;\; \mathrm{d}y \)

---

Does this look better?