Find ${\int }_0^{\pi /2} {\cos }^{11}xdx$

${\int }_0^{\pi /2} {\cos }^{n}xdx=\left\{\begin{array}{l}\frac{n-1}{n}\cdot \frac{n-3}{n-2}\dots \dots \dots \cdot \frac{1}{2}\cdot \frac{\pi }{2}\text{ if niseven }\\ \frac{n-1}{n}\cdot \frac{n-3}{n-2}\dots \dots \dots \frac{2}{3}\text{ if }n\text{ is odd }\end{array}\right.$

${\int }_0^{\pi /2} {\cos }^{11}xdx=\frac{10}{11}\times \frac{8}{9}\times \frac{6}{7}\times \frac{4}{5}\times \frac{2}{3}=\frac{256}{693}$