## anonymous 3 years ago im having trouble integrating the double iterated integral R= [0,3] X [0,rad(9-y^2)] and the function inside the integral is "y dy dx"

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1. anonymous

$\int\limits_{0}^{3}\int\limits_{0}^{\sqrt{9-7^{2}}} y dy dx$ thats the integral

2. anonymous

something's not right with either your limits or your order of integration...

3. anonymous

sorry your right.... its y dx dy

4. anonymous

if you're integrating in 'dy' .. your limits will be functions of x

5. anonymous

ok

6. anonymous

that works...

7. anonymous

integral of ydx is yx +C

8. anonymous

ive tried u sub...and integration by parts. but i just cant get the answer....

9. anonymous

still something weird about it though... shouldn't be written like that...

10. anonymous

the problem just says.... evaluate the iterated integral

11. anonymous

k

12. anonymous

they're writing it weird to try and throw you off I guess...

13. anonymous

anyway... plug in the limits on 'x' ... ( 0 ... srt(9-y^2) ) and then evaluate with respect to dy

14. anonymous

but then what? dont we need to simplifly

15. anonymous

so (y*sqrt(9-y^2) + C) dy

16. anonymous

you can use u sub.s ...

17. anonymous

9-y^2 = u -2y dy = du y dy = -du/2

18. anonymous

yes but then we need to plug in 3 into $\sqrt{9-3^{2}}$ wich equals 0 in the rad

19. anonymous

so?

20. anonymous

ends up canceling everything out.... and the answer is supposed to be 3

21. anonymous

...

22. anonymous

lower limit?

23. anonymous

is 0

24. anonymous

omg....

25. anonymous

ive done this problem like no lie 10 times and i never pluged in the lower limit = 0 giving me the right answer 9

26. anonymous

thank you so much for letting me realize this. how to i give a medal??

27. anonymous

click 'best response'