I'm curious to know the relationship between the determinant and the integration by using the area of the square
Let's say we have the following matrix.
$$
A = \begin{bmatrix} 2 & 0 \\ 0 & 2 \end{bmatrix} \\
det(A) = 2\*2 - 0\*0 = 4
$$

Now, the funciton is $f(x) = a$ where $a$ is the length of the square's sides. So, 
$$
f(x) = \int^2\_0 a dx = 2\*x \rvert^{2}\_{0} = 4
$$ 

where $a = 2$
Is there any article handles this topic? I mean the similarities between the determinant and the integration?
Thanks in advanced.