3. Convert the integral from rectangular coordinates to both cylindrical an spherical coordinates, and evaluate the simplest iterated integral. 1 1-y2
3. Convert the integral from rectangular coordinates to both cylindrical an spherical coordinates, and evaluate the simplest iterated integral. 1 1-y2
5. (15 points) Consider 3 dz r dr d, 20. a. Convert the integral to rectangular coordinates with the order d: dr dy (but don't evaluate.) b. Convert the integral to spherical coordinates (but don't evaluate.)
5. (15 points) Consider 3 dz r dr d, 20. a. Convert the integral to rectangular coordinates with the order d: dr dy (but don't evaluate.) b. Convert the integral to spherical coordinates (but don't evaluate.)
NOTE:
in spherical coordinates the volume is obtained by the sum of 2
iterated integrals
Also, please do your best with the handwriting. Thank you very
much :)
Part 1 Convert the rectangular coordinate integral to cylindrical coordinates and spherical coordinates and evaluate the simplest iterated integral: 13 x dz dy dx 14 x2+ y? dz dy de
Part 1 Convert the rectangular coordinate integral to cylindrical coordinates and spherical coordinates and evaluate the simplest iterated integral: 13 x dz...
5. In spherical coordinates evaluate the triple integral [ff (x2 + y2 +z?)2dV where D is the unit ball. (20 points)
A) solve this integral in cylindrical
coordinates.
b) set up the integral in spherical coordinates (without
solving)
10 points Compute the following triple integral: 1/ 1.32 + plav JD where D is the region given by V x2 + y2 <2<2. Hint: z= V x2 + y2 is a cone.
4. Evaluate the integral by changing to spherical coordinates. (15.8 #41-43) a2-x2-y2
4. Evaluate the integral by changing to spherical coordinates. (15.8 #41-43) a2-x2-y2
ser up the triple integral in spherical coordinates to express the volume inside of a cone phi = pi/6 , and inside a sphere p=5
E l the following integral in spherical coordinates. This integral calculates the volume of the four to the right which is not own scale sin dp op de SS I weapon - (Type an ca u sing as redes)
Using an integral in spherical coordinates, find the volume of a sphere of radius 2.
Set up the following integral in spherical coordinates, then integrate. CL * *zdedydz