x=7 dy dz dx = x Z=0 The given triple integral sss =49-x² Y = 7-8...
The figure shows the region of integration for the integral. fx, y, z dy dz dx 0 Jo Rewrite this integral as an equivalent iterated integral in the five other orders. (Assume yx) 6x and z(x)-36-) x. f(x, y, 2) dy dx dz x, , z) dz dx dy f(x, y, z) dz dy dx f(x, y, z) dx dy dz fx, y, z) dx dy dz J0 Jo Jo f(x, y, z) dz dx dy 0 0 f(x, y,...
write neatly and all steps 5. Given the triple integral SII, dy dz do = AS Ddydz dr. a) Neatly draw the region in the plane which corresponds to the outer double integral, i.e. draw this region: PIT . dzdz. To b) Neatly sketch the region corresponding to the triple integral.
Write an iterated integral for SSS fex,y,z) av. S = {(x, y, z): 0 sxs8,0 sy s5,0<zs (5 - 6x - 2y)} 5 S 5-6x - 2y f(x, y, z) dz dy dx 5 8 5 f(x, y, z) dz dy dx s 8 5 5 - 6x - 2y f(x, y, z) dz dy dx 5 666 8 5 5 - 6x - 2y f(x, y, z) dx dy dz
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.
ZA 5. Clearly construct a triple integral of the form $SS dz dy dx that can be used to find the volume of the solid beneath the plane z=1-y as shown in the diagram. Note that one side of the base is formed by y= Vx. Be sure to provide a sketch of the projection on the xy plane. You do not have to evaluate the integral. 1 z=1-y y=1 X
Find the volume of the given solid region in the first octant bounded by the plane 2x + 2y + 4z4 and the coordinate planes, using triple integrals 0.0(020 Complete the triple integral below used to find the volume of the given solid region. Note the order of integration dz dy dx. dz dy dx Use a triple integral to find the volume of the solid bounded by the surfaces z-2e and z 2 over the rectangle (x.y): 0 sxs1,...
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
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
(a) For the double integral pin2 (In 2)2-y I = ef+y* dx dy. i. Sketch the region of integration. ii. Show that I = (extu 2) (b) Using a triple integral, calculate the volume of the region in the first octant (x > 0, y > 0, z > 0), bounded by the two cylinders z2 + y2 = 4 and x² + y2 = 4.
Q3. Sketch the region of integration for the integral [5(8,19,2) dr dz dy. (2, y, z) do dzdy. Write the five other iterated integrals that are equal to the given iterated integral. Q4. Use cylindrical coordinates and integration (where appropriate) to complete the following prob- lems. You must show the work needed to set up the integral: sketch the regions, give projections, etc. Simply writing out the iterated integrals will result in no credit. frs:52 (a) Sketch the solid given...