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[SOLVED] Double integration and polar coordinates
Find the area inside both circles r = 1, and [tex] r = 2 sin \theta [/tex] by double integration in polar coordinates.
None
The way the problem is worded sounds a bit strange, but I believe they're asking me to find the area of a circle with radius [tex] r = 2 sin \theta [/tex] minus the area or the circle with radius r = 1. I think my main problem is the way I'm setting up the double integral. When I graphed the circle with radius [tex] r = 2 sin \theta [/tex] on my calculator, it didnt look anything like a circle. I graphed [tex] y = \sqrt{4sin^2 \theta - 4sin^2 \theta cos^2 \theta} [/tex]. Maybe I'm graphing it wrong but here's how I set up the integral:
[tex] \int^{2 \pi}_{0} \int^{2 sin \theta}_{1} r dr d \theta [/tex]
Any help is appreciated.
Homework Statement
Find the area inside both circles r = 1, and [tex] r = 2 sin \theta [/tex] by double integration in polar coordinates.
Homework Equations
None
The Attempt at a Solution
The way the problem is worded sounds a bit strange, but I believe they're asking me to find the area of a circle with radius [tex] r = 2 sin \theta [/tex] minus the area or the circle with radius r = 1. I think my main problem is the way I'm setting up the double integral. When I graphed the circle with radius [tex] r = 2 sin \theta [/tex] on my calculator, it didnt look anything like a circle. I graphed [tex] y = \sqrt{4sin^2 \theta - 4sin^2 \theta cos^2 \theta} [/tex]. Maybe I'm graphing it wrong but here's how I set up the integral:
[tex] \int^{2 \pi}_{0} \int^{2 sin \theta}_{1} r dr d \theta [/tex]
Any help is appreciated.