Evaluate the integralnbspint01 int0radic1-x2

Question

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.