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Finding the boundaries of the double integral where $D$ is bounded by . . . I'm trying to find the double integral of f(x, y) = y f (x, y) = y I'm so confused as to where to find the boundaries I can find the y y boundaries by setting y y equal to x − 20 x 20 and x−−√ x, but how can I find the x x boundaries? Did you graph the solutions to both equations?
Compute area and volume by evaluating double integrals Solution: We can view that the center of the sphere is at the origin (0, 0, 0), and so the equation of the sphere is x2 + y2 + z2 = a2 We then can compute the volume of the upper half part of the sphere and multiply our answer by 2 (or the portion in the first octant and multiply the answer by 8) √ = 8 a2 − x2 − y2dxdy = πa3
858 Chapter 15: Multiple Integrals - UC Davis 66 Find the volume of the solid bounded on the front and back by the planes x = on the sides by the cylinders y = ;sec x, above by the cylinder z = 1 + y2, and below by the xy-plane
Double Integrals over General Regions - NITK Find the volume of the solid whose base is the region in the xy plane that is bounded by the parabola y = 4 x2 and the line y = 3x; while the top of the solid is bounded by the plane z = x + 4
Section 14. 2: Double Integrals Over General Regions Simplify the calculation of an iterated integral by changing the order of integration Use double integrals to calculate the volume of a region between two surfaces or the area of a plane region Solve problems involving double improper integrals