Double intergral

  • Thread starter arl146
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  • #1
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Homework Statement


Consider the heat density function for a metal plate: x + y2 + x2

Find the total heat in the plate given that the plate resides in the region x≥0, y≥0, x2 + y2 ≥ 1


The Attempt at a Solution



i thought it was pretty straightforward. i did a double integral with both limits being 0 to 1 but my professor said the y limit is not to 1. what is the top limit then?
 

Answers and Replies

  • #2
ehild
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Find the total heat in the plate given that the plate resides in the region x≥0, y≥0, x2 + y2 ≥ 1

Are you sure you copied the last formula correctly? I would mean both x and y going to infinity.

ehild
 
  • #3
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should be less than or equal to 1
 
  • #4
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so is the upper limit of y just sqrt(1-x^2) ?
 
  • #5
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Correct
 
  • #6
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ok now i cant do the integral..


first step, integrate WRT y. so the function becomes x + (y^3)/3 + x^2
plugging the limits for y in:

[x + [ (1-x^2)^(3/2) / 3 ] + x^2] - x - 0 - x^2

so youre just left with [ (1-x^2)^(3/2) / 3 ]. how do you integrate that WRT x ??
 
Last edited:
  • #7
HallsofIvy
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Let [itex]x= sin(\theta)[/itex]. That's a pretty standard integral.
 

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