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Applications of integration

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Applications of integration

  1. 1. Applications of Integration<br />Volume Methods <br />
  2. 2. Variables<br />Integral- area which is being found for area/volume, dictated by two points on a graph from point A to B<br />F(x)=a,b<br />Revolve around the X-axis or Y-Axis <br />
  3. 3. Equations<br />Vdisc/washer= ∏r2 h<br />Vshell= 2 ∏rh<br />
  4. 4. Methods<br />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 <br />
  5. 5. Washer Method<br />is used when there are two solids within each other<br />Same equation as disc method<br />Top-bottom <br />
  6. 6. Shell Method<br />Used primarily when it is on the y-axis <br />Different equation than disc and washer<br />Can be used at any time<br />Remember! When rotated aroundthe x-axis the equation should be in terms of y. <br />
  7. 7. Remember!<br />To change the equation if on the y-axis <br />
  8. 8. Remember!<br />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<br />
  9. 9. Practice <br />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<br />