\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Consider the function \(f(x) = a \sqrt{x}\).
Find the value of \(a\) such that \(f(x)\) is a probability density function on the interval \([0, 4]\).

Capture an image of your work. AI teacher feedback takes approximately 10 seconds.