I have the following equations and trying to determine the value of $a$
$g(x) = ax$
$f(x) = -2(x-3)(x^2+1)$
I am trying to identify the unknown value of a > 0 such that the following holds: the region that is bounded by the y-axis, the plot of f(x), and the plot of the linear function g(x) = ax, has area exactly 6.
I know for a start that I need to start with calculating the intersection of the two graphs $a$ but i do not know how to set it up and proceed to solve the question.
this is a rough sketch of f(x) and y=x
But I can not find the answer as it is quite challenging.