5) (10pts) Change the integral from rectangular to an equivalent integral in polar coordinates and then evaluate. DRAW THE REGION IN XY PLANE (3pts!) ?_{-4}^{4} ?_{-sqrt{16-y^2}}^{0} frac{sqrt{x^2+y^2}}{1+sqrt{x^2+y^2}} dx dy
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In polar coordinates, x = rcos(θ) and y = rsin(θ). Also, the differential area element dxdy becomes rdrdθ in polar coordinates. The given integral is ∫∫(x^2 + y^2) dxdy over the region √(16 - y^2) / (1+√(r^2+y^2)). Substituting x = rcos(θ) and y = rsin(θ), we Show more…
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