University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

108

Pages:

1
Author:

Enrique Hendrix

Workshop #21 1. Change the order of integration by first sketching the region of integration. Then evaluate your integral, if possible. Z πZ π sin y (a) dydx y 0 x Z 9 Z − √y (b) f (x, y) dxdy 0 −3 2. Use a double integral to setup an integral which represents the area of the region bounded by y = (x − 1)2 , y = (x + 1)2 , and y = 0. (Sketch the region! ) 3. Use a double integral to setup an integral which represents the volume of the solid that lies below the surface x + y + z = 1 and above the region bounded by x = 0, y = 0, and x + y = 1. (Sketch the region! ) 4. Use a double integral to setup an integral which represents the volume of the solid that lies inside the sphere x2 + y 2 + z 2 = 2 and above the paraboloid z = x2 + y 2 (Sketch the region! ). Evaluate your integral.