Area Between Two Curves Recall that the area under a curve and above the xaxis can be computed by the definite integral. If we have two curves y = f(x) and y = g(x) such that
Example Find the area between the curves
Solution
= 1/3  1/4 = 1/12.
Exercises
Application Let y = f(x) be the demand function for a product and y = g(x) be the supply function. Then we define the equilibrium point to be the intersection of the two curves. The consumer surplus is defined by the area above the equilibrium value and below the demand curve, while the producer surplus is defined by the area below the equilibrium value and above the supply curve.
Example
f(x) = 1,000  0.4x^{2}
Solution We first find the equilibrium point: We set or We get We integrate
= 8400
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