# Math 22 The Area of a Region Bounded by Two Graphs

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## Area of a Region Bounded by Two Graphs

If and are continuous on and for all in , then the area of the region bounded by the graphs of given by

**Exercises**

**1)** Find the area of the region bounded by the graph of and the graph of .

Solution: |
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Find the bound of the region by setting , so , hence , then , therefore and |

Check which function is the top function by choosing one number in between the bound and plug in: |

Pick , so , and . Therefore, will be the top function. |

## Consumer Surplus and Producer Surplus

Given the demand function is and the supply function is . Let be the solution of . Then, the Consumer Surplus is and the Producer Surplus is

**Exercises**

**2)** Find the consumer and producer surpluses by using the demand and supply functions .

Solution: |
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Find the solution (equilibrium point): , so , so , then . Therefor, and |

So |

and |

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