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Evaluate given integral by changing to spherical coordinates

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Reference no: EM13848237

1. Evaluate the integral ∫01 ∫0√1-x2 ∫√x2+y2√2-x2-y2 xy dz dy dx by changing to spherical coordinates.

2. Evaluate the integral ∫∫∫E(x2 + y2) dV where E is the part of the sphere x2 + y2+z2 = 1 above the xy-plane.

3. Evaluate the integral ∫∫∫E √x2 + y2 dV where E is the solid in the first octant inside the cylinder x2 + y2 = 16 and below the plane z = 3.

Reference no: EM13848237

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