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- Since the R integration region is the region bounded by the hyperbolas x2 - y2 = 1, x2 - y2 = 9, xy = 4 and xy = 2 in the first region, with the help of u = xy and v = x2 - y2 transformation ∫∫R ( x2 + y2) dA What is the value of the integral?a) 0b) -7c) 7d) 8e) noneIntegrate f(x,y,z)=18xz over the region in the first octant (x,y,z > 0) above the parabolic cylinder z=y2 and below the paraboloid z=8-2x2-y2.Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.
- Solve the problem with complete solution and draw the figure. Determine the ordinate of the centroid of the area bounded by the curve x2 = 8y and the line 2x – y = 0.Find the centroid (x¯,y¯)(x¯,y¯) of the region bounded by: y=7x^2+2x, y=0, x=0, and x=9?Sketch the region of integration and evaluate the integral∫∫∫R xy dV where R is the solid tetrahedron with vertices (2,0,0), (3,3,0), (3,3,3) and (0,3,0).
- find the centroid of the area bounded by y^2=4x, the y axis and y-2=0 with complete solutionDetermine the centroid C (x,y) of the shaded region bounded by (y-20)^2 =16x, and the axes PS: its -16X not 16xFind the centroid of the region bounded by the graphs of the equations using any method y = √(1 − x2) , y = 0
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