14.3 Change of Variables, Polar Coordinates The equation for this surface is ρ= sinφ *cos(2θ) (in...
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Transcript of 14.3 Change of Variables, Polar Coordinates The equation for this surface is ρ= sinφ *cos(2θ) (in...
14.3 Change of Variables, Polar Coordinates
The equation for this surface is ρ= sinφ *cos(2θ) (in spherical coordinates)
The region R consists of all points between concentric circles of radii 1
and 3 this is called a Polar sector
A small rectangle in on the left has an area of dydxA small piece of area of the portion on the right
could be found by using length times width.The width is rdө the length is dr
Hence dydx is equivalent to rdrdө
Problem 18
Evaluate the integral by converting it to polar coordinates
Note: do this problem in 3 steps1. Draw a picture of the domain to restate
the limits of integration2. Change the differentials (to match the
limits of integration)3. Use Algebra and substitution to change
the integrand
Problem 22
Combine the sum of the two iterated integrals into a single iterated integral by converting to polar coordinates. Evaluate the resulting integral.