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Volume in a cone, using a double integral.

  • #1
127
0

Homework Statement


Evaluate the volume under z^2 = x^2 + y^2
and the disc x^2 + y^2 < 4.

Just wondering what I should write to constitute a proper solution. Would this do?:

V=(int)(int) z dA
R is {x²+y² < 4} [context: R in other problems was the region over which integrals were performed]

(int)(int) z dA
=
(int)(int) sqrt( r² ) r drdT [T for theta]
(using x²+y²=r² and dA->r dr dT)

The integral to actually be computed is:
(int)(int) r² dr dT
with r in [0,2]
T in [0, 2pi]
= 2pi/3 whatever the hell it is.

For a 1st year student in not-mathematics (which isn't me), is that too concise?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
Looks to me like it's got all the essential steps, given the abbreviations you are using like (int). If you aren't the 1st year student in not-mathematics, why are you asking?
 
  • #3
127
0
I need to know how to explain it to 1st year not-mathematics students.
 

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