Question

THEOREM6 Let f and g be continuous functions with (x) 2 g(x) over [a, b]. Then the area of the region between the two curves, from U(x) - g(x)]dx.

find the area of the region bounded by the graphs of the two equations below. How do you know where they intersect? How do you find the values of a and b? How do you know which is the upper graph and which is the lower graph? please explain how you got it thanks.

Answer 1

To find area bounded between 2 curves y = f(x) and y = g(x) from x = a to x = b is the area of the shaded region Area between 2 curves is lower part of upper graph intersection with upper part of lower graph. Here, upper graph is f(x) and lower graph is g(x). So, the region of intersection of lower part of f(x) and upper part of g(x) is the area between 2 curves f(x) and g(x) a and b will be given in question and f(x) is upper graph in interval [a, b] and g(x) is lower graph in interval [a, b] since f(x) > g(x) Forall h elementof [a, b] \r\n f(x) is called upper graph in interval [a, b] & g(x) is called lower graph is same interval [a, b] if f(x) greaterthanorequalto g(x) Forall x elementof [a, b] Now, Area of shaded region = int^b_a [f(x) - g(x)] dx