Notes for 13.3

# Notes for 13.3 - 3.1 becomes âˆ âˆ âˆ âˆ = R R d dr r dA...

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Calculus III – Section 13.3 – Change of Variables to Polar Form Some double integrals are MUCH easier to evaluate in polar form than in rectangular form. This is especially true for circular regions. Recall: Polar coordinates ( 29 θ , r of a point are related to the rectangular coordinates ( 29 y x , of the point as follows: x r y r r x y y x = = = + = cos , sin , , tan 2 2 2 Since we are now going to be looking at areas of sectors instead of rectangles, our area formula from section

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Unformatted text preview: 3.1 becomes âˆ« âˆ« âˆ« âˆ« = R R d dr r dA . Below is the graph of y x =-4 2 . Find the area bounded by the graph and y=0 using a double integral in rectangular coordinates and then find the area using a double integral in polar coordinates. x y-2.5-2-1.5-1-0.5 0.5 1 1.5 2 2.5 1 2 Now we will go back and do #50 in section 3.1 again. âˆ« âˆ«----2 2 4 4 2 2 dx dy x x 13.3.2 #14 #18 #32 #38...
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Notes for 13.3 - 3.1 becomes âˆ âˆ âˆ âˆ = R R d dr r dA...

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