## psk981 3 years ago integrate f(x,y)= x^2 +y over a triangular region bounded by (0,0), (1,0),(0,1)

1. TuringTest

draw the region, what is the equation of the line between (1,0) and (0,1) ?

2. psk981

|dw:1352136497588:dw|

3. TuringTest

yes

4. TuringTest

only reversed, gotta have the constant last or you won't get a constant as an answer!

5. psk981

how would my integrals look

6. TuringTest

the inner integral is bounded by the function -x, the outer by the constants

7. psk981

after i solve it i get 2/3

8. TuringTest

I get 3/4 can you show your work?

9. psk981

$\int\limits_{0}^{1} \int\limits_{0}^{-x} x^{2}+y dydx$ |dw:1352137141341:dw| |dw:1352137253709:dw|

10. TuringTest

|dw:1352137394567:dw|you dropped the /2 part...

11. psk981

ok sweet i got it

12. TuringTest

13. psk981

but order doesn't matter if you have constants

14. TuringTest

If both bounds are constants then often not, but sometimes the integral is only possible in a certain order. In this case we have the bounds as one constant, and one function. You could have done this one in the other order, but you would have to change the inner function to terms of yu.

15. TuringTest

terms of y*

16. TuringTest

@psk981 I just realized we messed this one up :P

17. TuringTest

|dw:1352139848664:dw|

18. psk981

how so

19. TuringTest

this function ain't -x, it's 1-x|dw:1352139902007:dw|

20. TuringTest

so that should be the inner bound

21. psk981

so goes from 0 to 1-x

22. TuringTest

yes

23. TuringTest

and|dw:1352140168346:dw|so I totally space out on the last one, sorry

24. TuringTest

$\int_0^1\int_0^{1-x}x^2+ydydx=\int_0^1\left.x^2y+\frac{y^2}2\right|_0^{1-x}dx$