The integral shown describes the volume of a bounded region in space. The ultimate goal here...

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The integral shown describes the volume of a bounded region in space. The ultimate goal here is to rewrite the region and the integral in both cylindrical and spherical coordinates, and also, given a density function, set up and compute the center of mass. This is super long and tedious, and the parts below are stepping you through this question, so please work through that as is appears. I 11% a) Write region in interval notation (? ≤x≤?, ?sys?, ?sz≤?) b) Sketch just the xy floor, and express the floor in polar to get things started (what are the bounds on r and ?): c) Sketch the xz / yz profile. √50-²-² √√x² + y² 1dz dy dx d) Convert the z bounds into polar/cylindrical (what's ? SzS?now, in terms of ?). e) At this point, you've got everything you need to write the integral in cylindrical coordinates, so do that: f) You've already got the spin for spherical (it's the same as the polar ), so all that's left are the radius p and tilt . Look at the profile. State the bounds on p and (?≤ps?, ?≤ø<?). g) And, write the integral in spherical coordinates. The integral shown describes the volume of a bounded region in space. The ultimate goal here is to rewrite the region and the integral in both cylindrical and spherical coordinates, and also, given a density function, set up and compute the center of mass. This is super long and tedious, and the parts below are stepping you through this question, so please work through that as is appears. I 11% a) Write region in interval notation (? ≤x≤?, ?sys?, ?sz≤?) b) Sketch just the xy floor, and express the floor in polar to get things started (what are the bounds on r and ?): c) Sketch the xz / yz profile. √50-²-² √√x² + y² 1dz dy dx d) Convert the z bounds into polar/cylindrical (what's ? SzS?now, in terms of ?). e) At this point, you've got everything you need to write the integral in cylindrical coordinates, so do that: f) You've already got the spin for spherical (it's the same as the polar ), so all that's left are the radius p and tilt . Look at the profile. State the bounds on p and (?≤ps?, ?≤ø<?). g) And, write the integral in spherical coordinates.

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Given b c I 5x0 Since Since 00 50xy i 510 and 1 dz dy dx ... View the full answer