## Calculus 10th Edition

$\dfrac {16}{35}\approx 0.457$
If $n$ is odd $(n\geq3)$ $$\Rightarrow \int ^{\pi /2}_{0}\cos ^{n}xdx=\left( \dfrac {2}{3}\right) \left( \dfrac {4}{5}\right) \left( \dfrac {6}{7}\right) \ldots \left( \dfrac {n-1}{n}\right)$$ $$\Rightarrow \int ^{\pi /2}_{0}\cos ^{7}xdx=\left( \dfrac {2}{3}\right) \left( \dfrac {4}{5}\right) \left( \dfrac {6}{7}\right) =\dfrac {16}{35}\approx 0.457$$