4. Given the integral 32-12 72 (4 1/16x² /132-x² - y2 z dzdy dx - 116xz...
4. Given it the integral 132-8272 CVT-xa AL z dzdy dx Vx?tyz 0 - 116=x2 b) Rewrite it in spherical wordinates
Do not evaluate, rewrite the integral using spherical coordinates 25-x² - y2 1 dz dx dy 05 NUS y=0 X-O Z=o
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...
10. Rewrite the following integral using cylindrical coordinates. Do NOT evaluate. V 25-y2 Lolo /x²+42 uz dz dx dy **
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)...
02. (10+10+5=25 points) The region E is the solid hemisphere x2 + y2 + 59.220 a) Evaluate 8zdV by using spherical coordinates. b) Evaluate SI, 8zdV by using cylindrical coordinates. c) Which coordinate system would you prefer for this integral and why? Explain. Can you evaluate every triple integral with both cylindrical and spherical coordinates? Explain.
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
C V I return K shift M 9e ation 14. Consider the triple integral dzdx dy representing a solid S. Let R be the projection of S onto the plane z=0. (a) Draw the region R. (b) Rewrite this integral SSls dzdy dx. as 15. Consider the transformation T: x = 2u + v, y = u + 20. (a) Describe the image S under T of the unit square R = {(u, u) | 0 using a change of...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
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...