2) 17 points) Express each integral as an equivalent integral with the other possible orders Sketch the solid and t...
please show all work in clean and legible handwriting with all
labels and steps that is properly explained for PROBLEMS #1, 2, 3,
AND 4. Any incorrect answers and not solving all 4 problems will
get an immediate thumbs down because they did not follow
directions, thank you
1) Express the triple integral Ⅲf (x,y,z) dV as an iterated integral in the two a) E={(x,y,z)Wr2+yszaj orders dzdy dr and dz dr dy where b) Sketch the solid region E c)...
Express the triple integral 2) d as an iterated integral in six different ways using different order of integration where T'is the solid bounded by the planes x = 0, y = 0,2-0 and + 4y + 5z = 12
2. (13 points) Let E be the solid region bounded by the planes x = 0, y = 0, 2=0, and x+y+z=1. (a) Sketch E. (b) Set up the integral SSSe ex+y+z dV as a triple iterated integral. (c) Compute the integral.
(5 pts each) Sketch the solid that is inside both z-x2+y 2. and x2 +y-4 with 1s z s 3. Then, given f(x.y,z) = x2 +y2+z2, use the specified coordinate system to set up the integral f(x.y,z)dV over the solid. using cylindrical coordinates а. b. using spherical coordinates
4. (5 points) Express the integral JI f(x, y, z) dV as an iterated integral in 6 different ways, where E is the solid region bounded by y2 + z-9. x--2, and x-2.
4. (5 points) Express the integral JI f(x, y, z) dV as an iterated integral in 6 different ways, where E is the solid region bounded by y2 + z-9. x--2, and x-2.
2. (12 points) By setting up and evaluating a triple integral, compute the area of the te by the coordinate planes 0.7 -0.2 0 and the plane + y +- eral, compute the area of the tetrahedron bounded
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,...
4,5 Sketch the solid whose volume is given by the iterated integral. 2-22 4. [1] 5 dydz de c2-y 5. (IT dx dz dy
solve problem 6
it is not a double integral, it is 1 integral
In Convert to cylindrical coordinates ſyddy Set up the integral) 1b. Convert to spherical coordinates JJ Jy daddy (Set up the integral) 2. Une cylindrical coordinates to determine the volume of the solid in the 1" octant enclosed by the coordinate planes, the cylinder + 16 and the plane (Set up - do not solve) 3. Use spherical coordinates to determine the volume of the solid that...
(2) In each case, sketch the region of integration, and write down the integral with the order of integration reversed: a,v) dydz;
(2) In each case, sketch the region of integration, and write down the integral with the order of integration reversed: a,v) dydz;