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1. Find the volume of the solid. Under the plane x +2y-z=0 And above the region bounded by y=x and y=x+.Using double integral.
4(a). Find the volume of the solid under the plane x + 2y - 2 = 0 and above the region bounded by y = 1, and y = (b). Evaluate the integral #/2
7. Set up and evaluate an integral that represents the volume of the solid under the plane y-z = 1 and above the bounded region enclosed by x 2y-y2 and x + y -4 For full credit, you must draw the region, find the points of intersection and show all steps. 7. Set up and evaluate an integral that represents the volume of the solid under the plane y-z = 1 and above the bounded region enclosed by x 2y-y2...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
Find the volume of the solid lying under the surface z = xy and above the rectangle [0,1] [0,2]. Evaluate the double integral where D is the region bounded by the y-axis, 2y = x, and y = 1. e-y²/2dA D
I need help with this question. I do not understand the role of the plane z=x+2y since boundary of x is [0,2] and y is [0,4]. Some concept clarification would be great. 2. (5 points) Sketch (rough sketch is ok) the solid that lies between the surface z r*+1 -0, x-2. У-0, and y-4 and the plane -x+2y and is bounded by the planes x Then, find its volume. 2. (5 points) Sketch (rough sketch is ok) the solid that...
Find the volume of the solid bounded above by the surface z = f(x,y) and below by the plane region R. f(x, y) = x2 + y2; R is the rectangle with vertices (0, 0), (9, 0), (9, 6), (0, 6) ( ) cu units
Find the volume of the given solid region bounded below by the cone z = \x² + y2 and bounded above by the sphere x2 + y2 + z2 = 8, using triple integrals. (0,0,18) 5) 1 x? +y? +22=8 2-\x?+y? The volume of the solid is (Type an exact answer, using a as needed.)
1. (10 points) Find the volume of the solid under the surface z = 1 +x2y2 and above the region of the xy-plane enclosed by x y2 and 1 1. (10 points) Find the volume of the solid under the surface z = 1 +x2y2 and above the region of the xy-plane enclosed by x y2 and 1
(6 points) 10. 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 + 6.