Application of Integrals

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Application of Integrals

  1. 1. Application of Integrals
  2. 2. Displacement vs. Total Time Traveled <ul><li>Displacement= ∫ b V(t) dt </li></ul><ul><ul><ul><ul><ul><li> a </li></ul></ul></ul></ul></ul><ul><li>Distance Traveled= ∫ b V(t) dt </li></ul><ul><ul><ul><ul><ul><li> a </li></ul></ul></ul></ul></ul>
  3. 3. Displacement vs. Total Time Traveled
  4. 4. Total Distance Traveled
  5. 5. Area Between Curves <ul><li>To find the area between two curves: </li></ul><ul><ul><li>Top – Bottom </li></ul></ul><ul><ul><li>Right - Left </li></ul></ul>*Make sure to use y boundaries and x=
  6. 6. Area Between Curves <ul><li>Examples: </li></ul>Determine the area of the region enclosed by and
  7. 7. Area Between Curves
  8. 8. Volume of a Solid of Revolution <ul><li>Disc Method: ∏ ∫ b (f(x))^2 dx; </li></ul><ul><ul><ul><ul><ul><li> a </li></ul></ul></ul></ul></ul><ul><ul><li>Ex. </li></ul></ul>
  9. 9. Volume of a Solid of Revolution <ul><li>Washer Method: V= ∏ ∫ b ((R)^2 -(r)^2) dx; </li></ul><ul><ul><ul><ul><ul><li> a </li></ul></ul></ul></ul></ul><ul><li>Around the x axis </li></ul><ul><ul><li>Y= dx (boundaries on the x axis) </li></ul></ul><ul><li>Around the y axis </li></ul><ul><li>x= dy (boundaries on the y axis) </li></ul>
  10. 10. <ul><li>Example: </li></ul>

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