Final answer:
To find the area enclosed by the two curves, set the equations equal to each other, find the x-coordinates of the points of intersection, and integrate the difference between the curves.
Step-by-step explanation:
To find the area enclosed by the two curves, we need to find the x-coordinates of the points where the curves intersect. We can do this by setting the two equations equal to each other:
x² - 10x + 6 = -x² - 4x + 22
By rearranging terms and solving for x, we find that x = 3 and x = 7. Now we can integrate the difference between the two curves from x = 3 to x = 7 to find the area:
A = ∫(x² - 10x + 6) - (-x² - 4x + 22) dx from 3 to 7
Calculating the definite integral gives us the area enclosed by the curves.