Evaluate the double integral ∬R(2x−y)dA, where R is the region in the first quadrant enclosed by the circle x^2+y^ 2= 4 and the
lines x = 0 and y = x, by changing to polar coordinates.
1 answer:
Answer:
Step-by-step explanation:
We are to integrate the function

over the area enclosed by the circle

Convert into polar coordinates

x=rcost and y = rsint
Since the lines are x=0 and y=x we find that t varies from 0 to pi/4

Double integral will become now

(since variables are independent here)
Substitute for r and t
4 sin pi/4 -2 cospi/4
= 
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Step-by-step explanation:
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Step-by-step explanation:


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