Final answer:
To find the area of the region enclosed by the two equations y = x and y = 5x - x², we need to find the points of intersection between these two curves and then integrate the difference between the two equations with respect to x. 10 square units.
Step-by-step explanation:
To find the area of the region enclosed by the two equations y = x and y = 5x - x², we need to find the points of intersection between these two curves. Setting the two equations equal to each other, we get x = 0 and x = 5. To find the area, we integrate the difference between the two equations with respect to x, from x = 0 to x = 5:
Area = ∫ [(5x - x²) - x] dx, from 0 to 5.
Evaluating the integral gives us Area = 10 square units.