Converting a triple integral from spherical to cartesian, cylindrical coordinates

[bfusco]

Homework Statement

Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ
-the bounds of the first integral (from left to right) are from 0 to pi
-the bounds of the second integral are from 0 to pi/2
-the bounds of the third integral are from 1 to 3

a)express I as an interated integral in terms of the cartesian coordinates x,y,z.
b)express I as an interated integral in terms of the cylindrical coordinates r, θ, z

Homework Equations

This is on a practice final i have soon so i would appreciate it if the aid given to me isn't spread across a few days. thank you in advance

 

[LCKurtz]

Homework Statement

Consider the interated integral I=∫∫∫ρ^3 sin^2(∅) dρ d∅ dθ
-the bounds of the first integral (from left to right) are from 0 to pi
-the bounds of the second integral are from 0 to pi/2
-the bounds of the third integral are from 1 to 3

a)express I as an interated integral in terms of the cartesian coordinates x,y,z.
b)express I as an interated integral in terms of the cylindrical coordinates r, θ, z

Homework Equations

This is on a practice final i have soon so i would appreciate it if the aid given to me isn't spread across a few days. thank you in advance

Do you mean right to left? Start by drawing, or at least describing the object, then we can talk.

 

[bfusco]

its pretty clear, as there are 3 integral signs, the left most integral has bounds 0 to pi, so on and so forth. this is the question as given to me on my practice final there is nothing more i can give you to describe the function.

 

[LCKurtz]

its pretty clear, as there are 3 integral signs, the left most integral has bounds 0 to pi, so on and so forth. this is the question as given to me on my practice final there is nothing more i can give you to describe the function.

My question about your limits would have been prevented by you using latex and putting the limits on the integrals. But putting that aside, what you have to do is use the limits to draw a picture of the object. That's the only way to figure out what the figure looks like and get the appropriate limits in the other coordinate systems.

 

[SammyS]

its pretty clear, as there are 3 integral signs, the left most integral has bounds 0 to pi, so on and so forth. this is the question as given to me on my practice final there is nothing more i can give you to describe the function.

LCKurtz was simply trying to help you out. How about saying: from outside to inside or from inside to outside ?

More pertinent questions to you are:

What have you tried?

Where are you stuck?​

According to the rules for Homework help on this Forum, You need to show your attempt at working the problem and/or give indication of making a serious effort at understanding the problem .

 

[bfusco]

lol i love when people recite what the rules of the forum are, i know he was only trying to help me but i didnt understand his response, i didnt feel like continuing so i went somewhere else with a slightly different question. had i had anything to give as far as my attempt at a solution i would have posted one, so there is no need for someone to attempt to take the "mature" person standpoint and imply that i have done something wrong. how are you suppose to put an attempt at the solution if you don't know where to start. so don't go reciting rules as if they arent already understood.

i needed help and i felt that my aid would have been more appropriate had i asked the questions in the steps recommended by my professor, i.e graph the function, determine the bounds, rewrite the equation, and so on. the only problem is i don't know anything about spherical coordinates so i thought a more appropriate place to start was from where i worded my other post.

 

[DryRun]

the only problem is i don't know anything about spherical coordinates

This forum section's purpose is explicitly labelled as "homework help" and not "teaching calculus for dummies". You will obviously not be able to do any questions if you do not understand the subject matter in the first place.

What you need is a proper introduction to the topic before attempting any questions. Read and learn from your notes or get a good book. You must at least form an idea of what spherical coordinates is all about. Familiarize yourself with the concepts and formulas. Study the examples in your notes/book. Then, look again at your question. At that point, if you still can't solve it, you'll be in a much better position to appreciate our help.

 

[berkeman]

lol i love when people recite what the rules of the forum are, i know he was only trying to help me but i didnt understand his response, i didnt feel like continuing so i went somewhere else with a slightly different question. had i had anything to give as far as my attempt at a solution i would have posted one, so there is no need for someone to attempt to take the "mature" person standpoint and imply that i have done something wrong. how are you suppose to put an attempt at the solution if you don't know where to start. so don't go reciting rules as if they arent already understood.

i needed help and i felt that my aid would have been more appropriate had i asked the questions in the steps recommended by my professor, i.e graph the function, determine the bounds, rewrite the equation, and so on. the only problem is i don't know anything about spherical coordinates so i thought a more appropriate place to start was from where i worded my other post.

Check your PMs.