Question
Asked Oct 22, 2019
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Evaluate the given integral by changing to polar coordinates.
64 x2 - y2 dA
R
where R =(x, y) I x2 + y2 s 64, x 2
1024t
X
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Evaluate the given integral by changing to polar coordinates. 64 x2 - y2 dA R where R =(x, y) I x2 + y2 s 64, x 2 1024t X

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Expert Answer

Step 1

x2 + y2 ≤ 64 = r2

Hence, r = 8

Under polar coordinates: x = rcosƟ; y = r sinƟ; dA = rdrdƟ

Step 2

The region R is semi circle of radius 8 lying in the first and the second quadrant such that x ≥ 0

Hence limits of integration will be from Ɵ = -π/2 to Ɵ = π/2  and r = 0 to 8

Step 3

If the desired area is A, then pease see the work...

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Tagged in

Math

Calculus

Integration