Integration of Determinants

\int {\left| {\begin{array}{ccccccccccccccc}
{f(x)}&{g(x)}&{h(x)}\\
a&b&c\\
p&q&r
\end{array}} \right|dx}  = \left| {\begin{array}{ccccccccccccccc}
{\int {f(x)dx} }&{\int {g(x)dx} }&{\int {h(x)dx} }\\
a&b&c\\
p&q&r
\end{array}} \right|

If the elements of any one row or any one column are variable and rest are constant, then only we apply this formula. Otherwise, we have to expand the determinants and then integrate.

Post Author: E-Maths