Final answer:
To find the area of the region enclosed by the curves and lines, set the two equations equal to each other and solve for x. Then, integrate the difference between the two curves over the appropriate intervals. Finally, calculate the definite integrals to find the enclosed area.
Step-by-step explanation:
To find the area of the region enclosed by the curves and lines, we first need to determine the points of intersection. We set the two equations equal to each other and solve for x:
4x + 13 = 2x + 49
2x = 36
x = 18
So the curves intersect at x = 18. Next, we integrate the difference between the two curves from x = 14 to x = 18, and from x = 18 to x = 22:
A = ∫(g(x) - f(x)) dx from 14 to 18 + ∫(f(x) - g(x)) dx from 18 to 22
Finally, we calculate the definite integrals to find the area enclosed by the curves and lines.