Question

Can anyone help me with a double integral question?

Answer 1

\[\int\limits_{?}^{?}\int\limits_{?}^{?}(5x^4y^3)/(x^5+1)dA\]

Answer 2

0<=x<=1 0<=y<=1

Answer 3

\[\int\int_D~\frac{5x^4y^3}{x^5+1}~dA\]
\[\int_{0}^{1}\int_{0}^{1}~\frac{5x^4y^3}{x^5+1}~dx~dy\]

Answer 4

i believe all that interprets to something along those lines

Answer 5

yep thats how it looks on my paper

Answer 6

since there is only one y part; lets flop the dxdy into dydx since the bounds are the same this only changes which one we do first and has no other effect

Answer 7

and lets add some brackets to divvy this up into more doable pieces
\[\int_{0}^{1}\left(\int_{0}^{1}~\frac{5x^4y^3}{x^5+1}~dy\right)~dx\]
\[\int_{0}^{1}\frac{5x^4}{x^5+1}\left(\int_{0}^{1}~y^3~dy\right)~dx\]
\[5\int_{0}^{1}\frac{x^4}{x^5+1}\left(\int_{0}^{1}~y^3~dy\right)~dx\]

Answer 8

ahhh that looks better already lol

Answer 9

do you see why i did that? or know why we can do that?

Answer 10

divide it up? because we have to do the parts separate right?

Answer 11

yes; and also, the "other" bits are constant when seen from the point of view of the part we are integrating with respect to; and constants can pull out.

Answer 12

and depending on which you do the other will act as constants

Answer 13

excellent :)

Answer 14

yep lol dident submit quick enough :)

Answer 15

ok so question

Answer 16

when can we take the y completly out without the x^3+1 denominator?

Answer 17

and, once we calculate the y part, its whole value is a constant so we can even rewrite this as

\[5~*~\int_{0}^{1}\frac{x^4}{x^5+1}dx~*~\int_{0}^{1}~y^3~dy\]

Answer 18

its a factor of the whole thing, imagine\[\frac{3*4}{2+7}=\frac{3}{2+7}*\frac{4}{1}\]

Answer 19

alright makes sense

Answer 20

so i did the y part and i got 1/4

Answer 21

1/4 is good for that

Answer 22

so would the integral now be \[\frac{ 5 }{ 4 }\int\limits_{0}^{1}\frac{ x^4 }{ x^5+1 }\]

Answer 23

yes, and as i stare at the, the 5 would be more useful inside the integral; that way the top is the derivative of the bottom

Answer 24

makes sense

Answer 25

AH YES I GOT IT!

Answer 26

lol thank you very much

Answer 27

:) youre welcome