## jedai17 2 years ago determine the limits and evaluate.. ∫∫x2y2dA where f is a figure bounded by F lines y = 1, y = 2 and x = 0, x = y

1. electrokid

|dw:1364052128248:dw| that gives you the limits

2. electrokid

it is easier to travel on y-axis because there is no sudden breaks

3. electrokid

so $0\le x\le y \qquad\text{&}\qquad1\le y\le2$

4. electrokid

if you are on the x-axis, you have to consider two pieces A) $$1\le y\le2 \qquad\text{&}\qquad0\le x\le1$$ B) $$x\le y\le2 \qquad\text{&}\qquad1\le x\le2$$ and sum them

5. electrokid

follow?

6. jedai17

in x=y, the value of y will become a and 2?

7. electrokid

"a"?

8. electrokid

all points on the "x=y" line will have the same abscissa and ordinate

9. jedai17

ah ok..

10. electrokid

yup, in the problem, all you need are the limits

11. jedai17

will i add these A) 1≤y≤2&0≤x≤1 B) x≤y≤2&1≤x≤2 ??

12. electrokid

use the first method its easier.

13. electrokid

yes those are your two regions for the second method

14. jedai17

x=0 to 1 and y= 1 to 2 ?

15. electrokid

no x=0 to y and y=1 to 2

16. electrokid

|dw:1364053324530:dw|

17. jedai17

i will integrate x^2y^2 using the limits x=0 to y and y=1 to 2 ?

18. electrokid

methid "1" is the horizontal element method "2" is the vertical

19. electrokid

yep. you got it

20. jedai17

ah ok.. in $\int\limits_{1}^{2}\int\limits_{0}^{y} x^2y^2 dxdy$, got 127/36.. is it right?

21. electrokid

$\int_{y=1}^2y^2\left[x^3\over3\right]_0^ydy={1\over3\times6}\left[y^6\right]_1^2$

22. jedai17

7/2?

23. electrokid

yep

24. electrokid

.. wait..

25. jedai17

ok..

26. electrokid

false alarm

27. electrokid

$dA=dxdy$

28. electrokid

kapeesh?

29. jedai17

127/36 = 3.53 7/2 = 3.5 my answer is 127/36 :)) its almost the same :)

30. electrokid

lol

31. jedai17

|dw:1364054668113:dw|

32. jedai17

@electrokid ? look at my answer?

33. electrokid

great job :D I'd personally not like to have many terms while integrating ... it gives migraine without it!

34. jedai17

thank you!so is my answer also correct?

35. electrokid

yep...

36. jedai17

thank you! tnx for ur time :)

37. electrokid

yer welcome :)