Use cylindrical coordinates to evaluate the triple integrals:
∫∫∫(x^(3) +xy^(2))dV, where Q is the solid in the
Q
first octant that lies beneath the paraboloid z=1-x^(2)-y^(2)
Please explain step by step

Question

Use cylindrical coordinates to evaluate the triple integrals:
∫∫∫(x^(3) +xy^(2))dV, where Q is the solid in the 
Q
first octant that lies beneath the paraboloid z=1-x^(2)-y^(2)
Please explain step by step

amistre64 · Answer

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amistre64 · Answer

i tend to get cyl and sphere coords mixed up; this tends to help

amistre64 · Answer

$$polar\to(r,\theta)$$
$$cylindar\to (r,\theta,z)$$

amistre64 · Answer

|dw:1334376165458:dw|
z = 0 to 1-x^2-y^2