CH. 6

CH. 6

1. 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)
                 • only if we want to
         • Limits are chosen to clearly see bottom being taken away from top function
           • to make math easier for people

2. 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

3. 6.3 Volumes by cylindrical Shells

   • Depends in which axis makes a cylindar.

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