Question

The value of ${\left({\int }_0^{\pi /6}se{c}^{2}xdx\right)}^2$ is:

Answer 1

${\int }_0^{\pi /6}se{c}^{2}xdx=[\tan x{]}_0^{\frac{\pi }{6}}=\frac{1}{\sqrt{3}}$

${\left({\int }_0^{\pi /6}se{c}^{2}xdx\right)}^2=(\frac{1}{\sqrt{3}}{)}^2=\frac{1}{3}=0.33$