CH. 6 - created from Mind Map

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

To find

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.

Disk

when f(x) or g(x) is 0

When we have a function that is not zero.....

Washer Method

Depends in which axis makes a cylindar.