Double Integrals: Solving Homework in 1st Quadrant

[joemama69]

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.

 

[tiny-tim]

Hi joemama69!

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?

 

[joemama69]

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

 

[tiny-tim]

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!

(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. )

 

[joemama69]

ya i noticed that, but i figured for my teachers sake i should do it thoroughly