Let D be the region enclosed by the two paraboloids z = 2x² + y² and z = 9-x²-8y2. Then the projection of D on the xy-plane is: None of these This option √²+x²51 ≤1 This option +y² ≤1
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- Suppose that a point (X,Y) is chosen at random from the region S on the xy-plane containing all points (x,y) such that x>= 0; y>= 0, and 6y+x<= 3. (a) Determine the joint p.d.f. of X and Y: (b) What is P(Y=X)? (c) What is P(X>=1)?S is the region bounded by paraboloid z=9-x^2-y^2 and the xy planeif d is the region in the first octant between the spheres x^2+y^2+z^2=1 and x^2+y^2+z^2=25 then. the rest of question in the following image
- calculate ∫ ∫ ∫Ty dv, being the T region inside the paraboloid z= 1/(x2+y2)the sphere x2+y2+z2=5Evaluate the double integral. ss 2y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1) DEvaluate the triple integral. (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2) and base vertices at (0, 0, 0), (2, 0, 0), (0, 2, 0), and (2, 2, 0)