calc 3 Find the volume of the solid that lies under the plane 4x+6y-22 + 15...
Problem 4. Find the volume of the solid that lies under the paraboloid 3 = x + y2 and above the region D in the ry-plane bounded by the line y = 2x and the parabola y = 1? Note: The region D is both of Type I and Type II.
7. Find the volume of the solid region that lies under the surface 2 = ry and over the region in the xy plane bounded by the curves y = 2r and y = r A. 4/3 B. 8 C. 8/3 D. 32/3 E. none of the above 8. Evaluate SSSE Vx2 + y2 dV where E is the region bounded by the paraboloid z = x2 + y2 and the plane z = 4. A. 87 B. 327 c....
multivariate calculus problem ..
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Find the volume of a solid that lies under the paraboloid z = 4-х._y' ' above the xy-plane and inside the cylinder x2 y 2y.
EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z 5x2 - 5y2, above the xy-plane, and inside the cylinder x2 + y2-2x (x-1)2 + y2=1 or r 2 cos 8 SOLUTION The solid lies above the disk D whose boundary circle has equation x2 +y2x or, after completing the square, In polar coordinates we have x2 +y Thus the disk D is given by and x-r cos(), so the boundary circle becomes 2r cos(), or...
please answer both questions
2. Find the volume of the solid that lies between the paraboloidand the plane -2x. Show your work by sketching the region. (8 pts.) 3. The region inside the curve r-2+sin 30 and outside the curve r 3-sin 30 consists of three same size pieces (draw the curves). Find the area of one of the pieces that lies in the first quadrant. Show your work. (8 pts.)
2. Find the volume of the solid that lies...
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
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 solid that lies above the paraboloid z = 22 + y2 and below the half cone z = 2² + y2.
(a) Find the volume of the solid under the paraboloid z x +3y2 and above the triangle with vertices (0,0), (4, 8), (8, 0). (b) Find the average value of (.y)-yover the rectangle with vertices (4,0), (-4,3), (4,3) (4, 0)
(a) Find the volume of the solid under the paraboloid z x +3y2 and above the triangle with vertices (0,0), (4, 8), (8, 0). (b) Find the average value of (.y)-yover the rectangle with vertices (4,0), (-4,3), (4,3) (4, 0)
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.