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πΆUnit 8

2 min readβ’june 8, 2020

Anusha Tekumulla

This topic is very similar to the previous two topics. However,Β this topic involves more steps. Normally, youβd integrate the function (top minus bottom) or (right minus left) from the endpoints provided. In the **situation where the curves intersect at more than two points**, you must use **additional steps**:Β

**Graph**the functions**Identify**the areas and what approach to take (either top minus bottom with vertical slices or right minus left with horizontal slices)Β**Set**the two equations equal to each other and find the intersection pointsΒ**Integrate**from the intersection points found in step 3 to find the area

If youβre still confused, take a look at this example:Β

Letβs say we want to find the area between y = sin(x) and y = -sin(x) from 0 to 2Ο.

- First, we
**graph the functions**. From this, we find that the functions intersect at more than the endpoints.Β - We have two areas, and
**the curves are on the top and bottom for both. Thus, we will use vertical slices to find the areas.Β** - Third, we
**set the functions equal to each other**to find the intersection point. Now, we know the intersection point is x = Ο.Β - Fourth, we
**integrate**(sin(x) - -sin(x)) from 0 to Ο to find the first area. Lastly, we**integrate**(-sin(x) - sin(x)) from Ο to 2Ο to find the second area.Β **Add them together**to get the final area.

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