Applications of integration kate roth

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Applications of integration kate roth

  1. 1. Kate Roth
  2. 2. Rectangular Approximation <ul><li>Definition: the sum of all individual rectangles. </li></ul><ul><li>Three different types </li></ul><ul><ul><li>LRAM ( L eft Endpoint R ectangular A pproximation M ethod) </li></ul></ul><ul><ul><li>RRAM ( R ight Endpoint R ectangular A pproximation M ethod) </li></ul></ul><ul><ul><li>MRAM ( M idpoint R ectangular A pproximation M ethod) </li></ul></ul><ul><li>In order to find the area, you must find the width of the rectangles in order to know how many there are going to be on the curved line. </li></ul>
  3. 3. LRAM (Left Endpoint Rectangular Approximation Method) <ul><li>LRAM is when the point is on the left side of the rectangle on the curve. </li></ul>
  4. 4. RRAM (Right Endpoint Rectangular Approximation Method) <ul><li>RRAM is when the point is on the right side of the rectangle of the curve. </li></ul>
  5. 5. MRAM (Midpoint Rectangular Approximation Method) <ul><li>MRAM is when the point is in the middle of the rectangle of the curved line. This method is the most accurate because it takes both the area above and below the curve. </li></ul>
  6. 6. Area <ul><li>In order to find the area between the curve and the x-axis, you must take the top curve subtracted by the bottom curve. </li></ul><ul><li>If you want to find the area between two curves on the x-axis, then you need to take the top curve subtracted by the bottom curve. </li></ul><ul><li>If you want to find the area between two curves on the y-axis, then you need to take the furthest right curve subtracted by the furthest left curve. </li></ul>
  7. 7. Volume <ul><li>Three Methods: </li></ul><ul><ul><li>Disk Method </li></ul></ul><ul><ul><li>Washer Method </li></ul></ul><ul><ul><li>Shell Method </li></ul></ul>Disk Method Washer Method Shell Method
  8. 8. Disk/ Washer Method <ul><li>These two methods use the same equation, only the disk method is used for one curve while the washer method is used for two curves. </li></ul><ul><li>These methods are best used when rotating around the x-axis </li></ul><ul><li>Equation: </li></ul>
  9. 9. Shell Method <ul><li>This method is best used when rotating around the y-axis. </li></ul><ul><li>Equation: </li></ul>

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