Es gilt für alle zum Ursprung punktsymmetrischen Funktionen $pp$: ${\displaystyle {\int }_{-a}^{0}p(x)\mathrm{d}x=-{\int }_0^{a}p(x)\mathrm{d}x}\backslash displaystyle\; \backslash int\_\{-a\}^0p(x)\backslash mathrm\{d\}x=\; -\backslash int\_0^a\; p(x)\; \backslash mathrm\{d\}x$.

Damit gilt für die Funktion $tt$:

${\displaystyle {\int }_{-a}^{a}t(x)\mathrm{d}x={\int }_{-a}^{0}t(x)\mathrm{d}x+{\int }_0^{a}t(x)\mathrm{d}x=-{\int }_0^{a}t(x)\mathrm{d}x+{\int }_0^{a}t(x)\mathrm{d}x=0}\backslash displaystyle\; \backslash int\_\{-a\}^a\; t(x)\backslash mathrm\{d\}x\; =\backslash int\_\{-a\}^0\; t(x)\backslash mathrm\{d\}x+\backslash int\_0^a\; t(x)\backslash mathrm\{d\}x=-\backslash int\_0^a\; t(x)\backslash mathrm\{d\}x+\backslash int\_0^a\; t(x)\backslash mathrm\{d\}x=0$