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Integrate w.r.t. k
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det(\left(\begin{matrix}k&1\\4&5\end{matrix}\right))
Find the determinant of the matrix.
k\times 5-4
For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.
5k-4
Multiply k times 5.