[tex]\\\int \limits_{-\sqrt{\frac{13}{2}}}^{\sqrt{\frac{13}{2}}} 9-x^2-(x^2-4)\, dx=\\ \int \limits_{-\sqrt{\frac{13}{2}}}^{\sqrt{\frac{13}{2}}} -2x^2+13\, dx=\\ \Big[-\frac{2x^3}{3}+13x\Big]_{-\sqrt{\frac{13}{2}}}^{\sqrt{\frac{13}{2}}} =\\ -\frac{2(\sqrt{\frac{13}{2}})^3}{3}+13\sqrt{\frac{13}{2}}-(-\frac{2(-\sqrt{\frac{13}{2}})^3}{3}-13\sqrt{\frac{13}{2}})=\\ [/tex][tex]\\-\frac{13\sqrt{\frac{13}{2}}}{3}+13\sqrt{\frac{13}{2}}-(\frac{13\sqrt{\frac{13}{2}}}{3}-13 \sqrt{\frac{13}{2}})=\\ -\frac{26\sqrt{\frac{13}{2}}}{3}+26\sqrt{\frac{13}{2}}=\\ -\frac{26\sqrt{\frac{13}{2}}}{3}+\frac{78\sqrt{\frac{13}{2}}}{3}=\\ \frac{52\sqrt{\frac{13}{2}}}{3}[/tex]
