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(Solved) The centroid of a region R in the my-plane having area A is the point with Cartesian coordinates (E, 3]) given by i=i/medmdy, y=ifydmdy. (The...


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Hi i was going over this question from a lecture for polar coordinates we substitute Cos and sin right? I'm unsure how to go about it

3. The centroid of a region R in the my-plane having area A is the point with Cartesian
coordinates (E, 3]) given by i=i/medmdy, y=iféydmdy. (The centroid would be the centre of mass if a plate in the shape of R was made
out of a uniform density material.) Find the centroid (LE, 37) of the circular sector given by the polar coordinate inequal—
ities, 0$TSR03 OSQSQO:
where 0 < 90 < 7r/ 2. You are given the area A = %R0290. Do the integrals in polar coordinates. Leave the answer as a pair of
Cartesian coordinates.

 


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