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- Find the average distance from the origin of a point between the two spheres x ^ 2 + y ^ 2 + z ^ 2 = 1 and x ^ 2 + y ^ 2 + z ^ 2 = 4 .Find the average value of f(x,y)=yx^2 over the rectangle RR with vertices (−2,0),(−2,5),(2,5),(2,0).Find the center of mass of a thin plate of density δ = 3 bounded by the lines x = 0,y = x, and the parabola y = 2 - x2in the first quadrant.
- find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x if δ (x,y)=6x+3y+3IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square 0<= x <= 1, 0<=y<=1, in the xy-planeFind the average value of f(y)=y sqrt(4-5y) on the interval [3,4]
- Find the average squared distance between the origin and thepoints on the paraboloid z = 4 - x2 - y2, for z ≥ 0.Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant density δgm/cm2 bounded by the lines x = 3 and y = 3 in the first quadrant.Find the moment of inertia of the region between the parabola y = 6 − x2 and the line y = 1 – 2x from x=0 to x=2 with respect to y-axis.