1. Applications of Integration Volume Methods

2. Variables Integral- area which is being found for area/volume, dictated by two points on a graph from point A to B F(x)=a,b Revolve around the X-axis or Y-Axis

3. Equations Vdisc/washer= ∏r2 h Vshell= 2 ∏rh

4. Methods Disc Method - Disc method is used with hollow solids when finding volume-top-bottom - be sure to determinewhich graph is on top and which is on thebottom

5. Washer Method is used when there are two solids within each other Same equation as disc method Top-bottom

6. Shell Method Used primarily when it is on the y-axis Different equation than disc and washer Can be used at any time Remember! When rotated aroundthe x-axis the equation should be in terms of y.

7. Remember! To change the equation if on the y-axis

8. Remember! You can determine which graph is on top and which is on the bottom by plugging in a number which is in the interval and the bigger of the two is the one on top

9. Practice X2-9=f(x) 1) Graph the function 2) Find the Interval (-3,3) 3) Set Up the Integral∏∫ X2-9 (a,b = -3,3) 4) Solve using Calculator 5) Don’t forget units