Notes for 13.1,13.2 - A dx dy h y h y c d = z z 1 2 ( ) ( )...

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Calculus III – Section 13.1 – Iterated Integrals and Area in the Plane Just as we could take the derivative with respect to any variable in Chapter 12, we can also take the integral with respect to any variable by holding the others constant. #6 #16 Now let’s look at what this means graphically. In Calculus I you learned how to find the area between curves in the plane using the integral. You can also find the area in the plane using iterated integrals. Area of a Region in the Plane 1) If your region is vertically simple then A dy dx g x g x a b = z z 1 2 ( ) ( ) . 2) If your region is horizontally simple then
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Unformatted text preview: A dx dy h y h y c d = z z 1 2 ( ) ( ) . #31 Iterated integrals can be used for things other finding the area. Depending on the function you are integrating, it may be helpful to switch the order of integration. #40 #50 Calculus III Section 13.2 Double Integrals and Volume Volume of a Solid Region If f is integrable over a plane region R and f x y , b g for all x y , b g in R , then the volume of the solid region that lies above R and below the graph of f is defined as V f x y dA R = zz ( , ) . #14 #26 #34 #38...
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Notes for 13.1,13.2 - A dx dy h y h y c d = z z 1 2 ( ) ( )...

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