For the region R below, write \int \int_Z f dA

babeeb0oL 2021-09-11 Answered

For the region R below, write ZfdA as an integral in polar coordinates.image

Use t for θ in your expressions.

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Expert Answer

estenutC
Answered 2021-09-12 Author has 81 answers
From the given figure, it is seen that the region R is bounded by two circles, x2+y2=9andx2+y2=16
Therefore, region R can be defined as
R={(r,θ)3r4,0θπ}
it is known that,
RfdA=θ1θ2f(rcosθ,rsinθ)rdrdθ
Therefore, in polar co-ordinate,
RfdA=0π34f(rcosθ,rsinθ)rdrdθ (i)
Thus, comparing (i) with RfdA=0π34f(rcosθ,rsinθ)rdrdθ it is inferred that
a = 0
b=π
c = 3
d = 4
With dA=rdrdθ
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