Presentation on theme: "7.5 Area Between Two Curves"— Presentation transcript:
1 7.5 Area Between Two Curves Find Area Between 2 CurvesFind Consumer SurplusFind Producer Surplus
2 Area between 2 curves Let f and g be continuous functions and suppose that f (x) ≥ g (x) over the interval [a, b]. Then thearea of the region between the two curves, fromx = a to x = b, is
3 Example: Find the area of the region that is bounded by the graphs of First, look at the graphof these two functions.Determine where theyintersect.(endpoints not given)
4 Example (continued):Second, find the points of intersection by setting f (x) = g (x) and solving.
5 ò Example (concluded): Lastly, compute the integral. Note that on [0, 2], f (x) is the upper graph.(2x+1)-éëùûòd=3êúæèçöø÷48
6 DEFINITION:The equilibrium point, (xE, pE), is the point at which the supply and demand curves intersect.It is that point at whichsellers and buyers cometogether and purchasesand sales actually occur.
7 DEFINITION:Suppose that p = D(x) describes the demand function for a commodity. Then, the consumer surplus is defined for the point (Q, P) as
8 Example: Find the consumer surplus for the demand function given by When x = 3, we have Then,ConsumerSpl=Dx()d-E×ò52341+
9 Example(concluded):p. 453, formula 12, there is no “+C”
10 DEFINITION:Suppose that p = S(x) is the supply function for a commodity. Then, the producer surplus is defined for the point (Q, P) as
11 ò ( ) Example : Find the producer surplus for Find y when x is 3. When x = 3, Then,ProduceSpls=xE×-()ò3152+