Multivariable Calculus

Multivariable Calculus, HW 3 Name and Panther ID: 1.Reverse the order of integration and evaluate Z πZ π sin y dydx y 0 x 2. Evaluate the double integral in polar coordinates that provides the volume of the space region above the xy-plane inside the cylinder x2 + y 2 − x = 0 and bellow z = 1 − x2 − y 2 . 3. Set up and evaluate the triple integral for the volume of the solid enclosed between the cylinders x2 + y 2 = 1 and x2 + z 2 = 1. RRR 4. Use cylindrical coordinates to evaluate the integral zdxdydz, where T is T bounded above by the sphere x2 +y 2 +z 2 = 2 and below by the paraboloid z = x2 +y 2 . 1
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