## kevin7ama 2 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. kevin7ama

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

2. Algebraic!

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

3. kevin7ama

sorry your right.... its y dx dy

4. Algebraic!

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

5. Algebraic!

ok

6. Algebraic!

that works...

7. Algebraic!

integral of ydx is yx +C

8. kevin7ama

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

9. Algebraic!

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

10. kevin7ama

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

11. Algebraic!

k

12. Algebraic!

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

13. Algebraic!

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

14. kevin7ama

but then what? dont we need to simplifly

15. Algebraic!

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

16. Algebraic!

you can use u sub.s ...

17. Algebraic!

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

18. kevin7ama

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

19. Algebraic!

so?

20. kevin7ama

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

21. Algebraic!

...

22. Algebraic!

lower limit?

23. kevin7ama

is 0

24. kevin7ama

omg....

25. kevin7ama

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. kevin7ama

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

27. Algebraic!

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