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Double integrals

  • Thread starter joemama69
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  • #1
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Homework Statement



integrate y DA over the regions s, where s is in the first quadrant bounded by x = y^2 and x = 8 - y^2

Homework Equations





The Attempt at a Solution



If the y wasnt there i would evaluate two integrals and subtract them to get the area.
But since the y is there, can i still evaluate them seperatly with the y in place and subtract.
 

Answers and Replies

  • #2
tiny-tim
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Hi joemama69! :smile:
integrate y DA over the regions s, where s is in the first quadrant bounded by x = y^2 and x = 8 - y^2
and which axis??

If the y wasnt there i would evaluate two integrals and subtract them to get the area.
But since the y is there, can i still evaluate them seperatly with the y in place and subtract.
(not sure what you're subtracting, but:) yes … what's worrying you about that? :smile:
 
  • #3
399
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ya i was thinkin to hard

heres what i did, i broke it into two intigrals and added them

first intigral

i differentiated y dy from 0 to x^(1/2)
then i did in trems of x from 0 to 4 and got an area for 4

2nd integral

i differentiated y dy from 0 to (8-x)^(1/2)
then i did in trems of x from 4 to 8 and got an area for 4

4 + 4 = 8 is that right
 
  • #4
tiny-tim
Science Advisor
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ya i was thinkin to hard

heres what i did, i broke it into two intigrals and added them

4 + 4 = 8 is that right
Yup, that's fine! :biggrin:

(though you could have saved a little work by pointing out that the region was obviously symmetric about x = 4, so all you had to do was evaluate one integral, and then double it. :wink:)
 
  • #5
399
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ya i noticed that, but i figured for my teachers sake i should do it thoroughly
 

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