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13.1 Iterated Integrals and area in plane

13.1 Iterated Integrals and area in plane. Evaluate an iterated integral Use an iterated integral to find the area of a plane region. Recall from Calculus I and II…. Hint: Use u-sub. Hint: Use integration by parts!. When domain is rectangular where a<=x<=b and c<=y<=d.

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13.1 Iterated Integrals and area in plane

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  1. 13.1 Iterated Integrals and area in plane Evaluate an iterated integral Use an iterated integral to find the area of a plane region

  2. Recall from Calculus I and II…

  3. Hint: Use u-sub.

  4. Hint: Use integration by parts!

  5. When domain is rectangular where a<=x<=b and c<=y<=d

  6. Note: We use this notation as long as we haven’t chosen an order of integration (“dxdy” or “dydx”)

  7. What happens if domain isn’t so nice? (aka…not rectangular?)

  8. 13.2 Double Integrals and Volume Use double integral to represent the volume of a solid region Use properties of double integrals Evaluate a double integral as an iterated integral

  9. Geometrically, what does it mean??Vertically Simple

  10. Geometrically, what does it mean? Horizontally Simple

  11. Write domain as a vertically/horizontally simple domain. Then set up iterated integral

  12. Which way to slice? Which one is more ideal?

  13. Homework Pg. 942 #1-19 odd, 23, 27-31 odd, 33, 35, 39, 47, 49, 51, 59, 61 pg. 952 #

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