12030333
Description
Mind Map by Meri perkins, updated more than 1 year ago
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Created by Meri perkins
about 6 years ago
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CH. 6
- 6.1 Area between two curves
- Calculate area between two curves
- To add tiny rectangles between curves
- LIMITS OF INTEGRATION
- Where two functions are touching, intersecting.
- Given or Found
- To find
- we can think of area equation as a new function
- h(x)= fsub1(x)- fsub2(x)
- then take integral of this function
- no matter what the "top function" must be fsub1(x)
- no matter what the "top function" must be fsub1(x)
- then take integral of this function
- only if we want to
- h(x)= fsub1(x)- fsub2(x)
- we can think of area equation as a new function
- To find
- Given or Found
- Limits are chosen to clearly see bottom being taken away from top function
- to make math easier for people
- to make math easier for people
- Where two functions are touching, intersecting.
- LIMITS OF INTEGRATION
- To add tiny rectangles between curves
- Calculate area between two curves
- 6.2 Volumes by Slicing, DIsks, Washers
- Depending on which axis we rotate, we will find a particular
Volume
- Idea of Slicing:
- Each rotation forms an object
- Slice this object into little slivers perpendicular to x or y axis
- Volume by slicing
- V= intregral on a<b of A(x)
- This is the volume of each slice
- Rotate 180 deg. and ^2 our fsub1(x) and fsub2(x)
- If we made an h(x), square it.
- Disk
- when f(x) or g(x) is 0
- When we have a function that is not zero.....
- Washer Method
- Washer Method
- When we have a function that is not zero.....
- when f(x) or g(x) is 0
- Disk
- If we made an h(x), square it.
- Rotate 180 deg. and ^2 our fsub1(x) and fsub2(x)
- This is the volume of each slice
- V= intregral on a<b of A(x)
- Volume by slicing
- Slice this object into little slivers perpendicular to x or y axis
- Each rotation forms an object
- Idea of Slicing:
- Depending on which axis we rotate, we will find a particular
Volume
- 6.3 Volumes by cylindrical Shells
- Depends in which axis makes a cylindar.
- Depends in which axis makes a cylindar.
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