Question on triple integral polar

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SUMMARY

The discussion centers on calculating the mass of a solid defined by the equations x = (4 - y²)^(1/2), y = 0, z = 0, and z = 1 + x, with a density function of y. The key point of contention is the limits of integration for the polar coordinates, specifically whether the angle θ should range from -π/2 to π/2 or from 0 to π/2. The consensus is that the limits should indeed be from -π/2 to π/2, as the solid is bounded by y = 0, which necessitates including negative values of y in the polar transformation.

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yopy
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Find the mass of a solid bounded by
x = (4-y2)1/2
y = 0
z = 0
z = 1 + x
with density = y

i understand how to set it upand transform to polar and how to do it but my teacher said its supposed to be -pi/2 to pi/2 for the integral with respect to theta. shouldn't it be 0 to pi/2 because its bounded by y = 0?
 
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Maybe "y=0" should be "x=0"? The given equations don't seem to make sense without x=0 being included.
 

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