6.1 Area between two curves
6.2 Volumes by Slicing, DIsks, Washers
6.3 Volumes by cylindrical Shells
Calculate area between two curves
To add tiny rectangles between curves
LIMITS OF INTEGRATION
Where two functions are touching, intersecting.
Limits are chosen to clearly see bottom being taken away from top function
Given or Found
we can think of area equation as a new function
h(x)= fsub1(x)- fsub2(x)
only if we want to
then take integral of this function
no matter what the "top function" must be fsub1(x)
to make math easier for people
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.
when f(x) or g(x) is 0
When we have a function that is not zero.....
Depends in which axis makes a cylindar.