Answer to Question #289992 in Calculus for Ping

Question

Multiple integrals 1. Find the volume of the first octant part of the solid bounded by the cylinders C1 and C2 given by: C1 = { (x, y, z) ∈ R^3 : x^2 + y^2 = 16} and C2 = { (x, y, z) ∈ R^3 : y^2 + z^2 = 16 }. 2. Evaluate the line integral Z γ 4xydx + 3x^2 dy, where γ is the positively oriented boundary of the region R which is bounded above by the line y = 2x and below by the parabola y = x(x − 4) (Hint: use Green’s Theorem). 3. A solid ball B in R3 is bounded by a sphere of radius 9. Use triple integration to show that B has volume: V(B) = 972π.