${\displaystyle {}\int _{0}^{c}x^{2}\,dx=17\,.}$

Dabei ist

${\displaystyle {}\int _{0}^{c}x^{2}\,dx={\frac {1}{3}}x^{3}|_{0}^{c}={\frac {1}{3}}c^{3}\,.}$

Also ist

${\displaystyle {}c={\sqrt[{3}]{51}}\,.}$

${\displaystyle {}y}$

${\displaystyle {}d}$

${\displaystyle {}x}$

${\displaystyle {}-{\sqrt {d}}}$

${\displaystyle {}{\sqrt {d}}}$

${\displaystyle {}2{\sqrt {d}}d-\int _{-{\sqrt {d}}}^{\sqrt {d}}x^{2}\,dx=13\,.}$

Hierbei ist

${\displaystyle {}\int _{-{\sqrt {d}}}^{\sqrt {d}}x^{2}\,dx={\frac {1}{3}}x^{3}|_{-{\sqrt {d}}}^{\sqrt {d}}={\frac {1}{3}}{\sqrt {d}}^{3}\,.}$

Die Bedingung wird daher zu

${\displaystyle {}13=2{\sqrt {d}}d-{\frac {1}{3}}{\sqrt {d}}^{3}={\frac {5}{6}}{\sqrt {d}}^{3}\,.}$

Also ist

${\displaystyle {}d={\sqrt[{3}]{\frac {78}{5}}}\,.}$