Areas of Regions between Two Curves If f and g are continuous on [a,b] and g(x) ≤ f (x) for all x in [a,b], then the area of the
reiogn bounded by the graphs of f and g and the vertical lines x=a and x=b is
b
A = ∫ [ f (x) − g(x)]dx
a
Find the area of the region bounded by f (x) = 2 − x 2 and g(x) = x
First we must graph both curves.
Then we must find the points of intersection of the two curves.
These will be the lower and upper bounds of our integral. We must see which curve is on
top of the other to know which one should be subtracted from which. Then evaluate the
integral.
Find the area of the region bounded by f (x) = 3x 3 − x 2 − 10x and g(x) = −x 2 + 2x
First:
Then
Then