$\text{ If }f\left(x\right)=\left|\begin{array}{ccc}x& \cos x& e^{x^6}\\ {\sin }^{5}x& x^4& \sec x\\ {\tan }^{3}x& 10& 20\end{array}\right|,\text{ then the value of }{\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}} f\left(x\right)\mathrm{d}x =$

$\begin{array}{l}\text{ Given that }f\left(x\right)=\left|\begin{array}{ccc}x& \cos x& e^{x^6}\\ {\sin }^{5}x& x^4& \sec x\\ {\tan }^{3}x& 10& 20\end{array}\right|\\ \Rightarrow f\left(-x\right)=\left|\begin{array}{ccc}-x& \cos x& e^{x^6}\\ -{\sin }^{5}x& x^4& \sec x\\ -{\tan }^{3}x& 10& 20\end{array}\right|\\ =-f\left(x\right)\\ \therefore f\left(x\right)\text{ is an odd function }\\ \therefore {\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}} f\left(x\right)\mathrm{d}x=0\left(\because {\int }_{-a}^a f\left(x\right)\mathrm{d}x=0,\text{ when }f\left(x\right)\text{ is odd function }\right)\end{array}$

Therefore, the correct answer is 0000.00