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**Week 11: Area between curves**

To find the **area between** two **curves** defined by functions, integrate the difference of the functions. If the graphs of the functions cross, or if the **region** is complex, use the absolute value of the difference of the functions. In general, **two graphs** y=f(x) and y=g(x) may cross. Sometimes f(x) may be larger and sometimes g(x) may be larger. In order to **find** the **area enclosed** by the **curves**, we can **find** where f(x) is larger, and where g(x) is larger, and then take the appropriate integrals of f(x)−g(x) or g(x)−f(x) respectively.Finally, unlike the **area** under a **curve** that we looked at in the previous chapter the **area between** two **curves** will **always** be **positive**. If we get a negative number or zero we can be sure that we've made a mistake somewhere and will need to go back and find it.