ZA 5. Clearly construct a triple integral of the form $SS dz dy dx that can...
Clearly construct a triple integral of the form dz dy dx to find the volume of the nose of a vehicle constructed from the paraboloid y=2(x +z) and the vertical plane y=6. But do not evaluate the integral.
y2 + 4z2 = 16 Clearly construct a triple integral of the form dz dy dx to find the volume of the solid shown. The upper surface is defined by the cylinder y? +422 = 16. But do not evaluate the integral. 4 x
8. Clearly construct a triple integral of the form dz dy dr to find the volume of the solid shown. The solid is constructed by taking the paraboloid :=x2 + y and have the top cut by the plane z=4y. But do not evaluate the integral. 1 10 8 ry
please provide algebric details 7. Clearly construct a triple integral of the form dz dy dx to find the volume of a solid constructed by joining 2 paraboloids J==18- x - y? . But do not have to evaluate the integral. (==x² + y² 2-18-x - y
4. Rewrite the following triple integral so that the order of integration is dy dx dz. Do not evaluate it. (3x + y) dz dy dit
x=7 dy dz dx = x Z=0 The given triple integral sss =49-x² Y = 7-8 L dydzdx a) draw the region of integration for this double integral in the Zx plane 5*=7 62-4 dzdx z=0 b) Sketch the region corresponding to the triple integral SZ=49-x²
2 147 a. Evaluate the triple integral (convert to oylindrical)12I, J xz dz dx dy b. Find the moment of inertia about the z-axis for the solid in the first octant bounded by x2+y2 -4 and z2-x2 + y2 if the density is given by: z. (Use cylindrical.) c. Find the mass of the solid bounded by z2 -x2 +y2 and z 1 in the first octant, if the density is given by: cos. (Use spherical.) 2 147 a. Evaluate...
QUESTION 2 Solve the problem. Write an iterated triple integral in the order dz dy dx for the volume of the tetrahedron cut from the first octant by the plane yz + 9(1 -y/10)3(1 -x/9-y/10) a dz dy dx 0 0 0 10(1 -x/9) ,3(1-x/9-y/10) 9 dz dy dx 0 0 1-x/9-y/10 C.9 1 -y/10 dz dy dx 0 0 0 d. 9 1 -x/9 1-x/9-y/10 dz dy dx 0 0 0
16. o integrad [**** The triple da dy dz describes the solid pictured at right. Rewrite as an equivalent triple integral in the following orders (DO NOT EVALUATE): 31 (a) dy dz dx (b) du dz dy 2. 16-2 21. Given dy da, 16- (a) Sketch the region of integration and write an equivalent iterated integral in the order dx dy. (You do not need to evaluate it!) (b) Now write it as an equivalent iterated integral in polar coordinates....
please show complete work 25) Use a triple integral in the coordinate system of your choice to find the volume of the solid in the first octant bounded by the three planes y =0 z 0, and z 1-x x y2. Include a sketch of the solid as well as appropriate projection and an Hint: for rectangular coordinates, use dV might not be given in the exam dz dy dx. This hint 25) Use a triple integral in the coordinate...