Final answer:
The finite region between the curves y = mx and y = x² - 1 can be found by determining the points of intersection between the two curves.
Step-by-step explanation:
The finite region between the curves y = mx and y = x² - 1, where m is a positive constant, can be found by determining the points of intersection between the two curves. To do this, set the two equations equal to each other:
mx = x² - 1
Rearrange the equation to get:
x² - mx - 1 = 0
Solve this quadratic equation for x:
x = (m ± √(m² + 4))/2
The finite region is the area between the x-values of the two points of intersection.