kevin7ama
im having trouble integrating the double iterated integral
R= [0,3] X [0,rad(9y^2)]
and the function inside the integral is "y dy dx"



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kevin7ama
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\[\int\limits_{0}^{3}\int\limits_{0}^{\sqrt{97^{2}}} y dy dx\]
thats the integral

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

kevin7ama
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sorry your right.... its y dx dy

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

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ok

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that works...

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integral of ydx is yx +C

kevin7ama
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ive tried u sub...and integration by parts. but i just cant get the answer....

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

kevin7ama
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the problem just says.... evaluate the iterated integral

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k

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

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

kevin7ama
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but then what? dont we need to simplifly

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

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you can use u sub.s ...

Algebraic!
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9y^2 = u
2y dy = du
y dy = du/2

kevin7ama
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yes but then we need to plug in 3 into \[\sqrt{93^{2}}\] wich equals 0 in the rad

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so?

kevin7ama
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ends up canceling everything out.... and the answer is supposed to be 3

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...

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lower limit?

kevin7ama
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is 0

kevin7ama
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omg....

kevin7ama
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ive done this problem like no lie 10 times and i never pluged in the lower limit = 0 giving me the right answer 9

kevin7ama
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thank you so much for letting me realize this. how to i give a medal??

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click 'best response'