Application of integrals flashcards


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Application of integrals flashcards

  1. 1. Application of Integrals Flashcards<br />
  2. 2. Washer Method<br />
  3. 3. Washer Method is used to find the volume between two curves that are rotated about the x-axis or the y-axis. The method involves integrating the area of the cross-sections which is a circle without a center. The formula for either rotation is basically <br />With y-axis rotation, f(x) in the formula represents the function furthest right and g(x) represents the inner function (aka the one furthest left).<br />With x-axis rotation, f(x) represents the function that is on top while g(x) represents the function that is closer to the x-axis (the bottom function).<br /> The cross-section<br />
  4. 4. Inverse Area Method<br />
  5. 5. The inverse method is used to find the area between two curves when it is difficult to use the x-axis method or the y-axis method. This method requires that the functions be rewritten in inverse form ( so you switch the x’s& y’sand solve to isolate y). Graph out the new equations. Then you take the integral of the curve on top minus the curve on bottom on interval.<br />
  6. 6. Shell Method<br />
  7. 7. The Shell Method is also used to find the volume of a function or between two functions rotated around an axis or a line. The tricky part with this method is that it switches the variable of integration. So if you’re rotating about the x-axis then the shell method is written with the equations using y and vice versa. The formula for shell method is<br />The variable r represents the radius of the shell which is just the simple variable of integration either x or y depending on the problem. Unless its rotated around a line then it’s a number minus the x/y.<br />The h represents the height of the shell which is the function itself. If you’re finding the area between two functions around then h represents the function on top minus the function on bottom.<br />The w represents the thickness of the shell which is just dx or dy. <br />
  8. 8. Which method of rectangular approximation does this this graph use?<br />
  9. 9. Left Rectangular Approximation<br />LRAM<br />
  10. 10. Disk Method<br />
  11. 11. Disk Method is used to find the volume of a single function rotated about either the y-axis of the x-axis. Once a function is rotated about an axis we can take the integral of it’s cross-section to find the volume. The cross-section of a single function rotated would be a circle. So to find the volume, this formula is used <br />