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Set Up an Integral for Both Orders of Integration, and Use

Question 48

Multiple Choice

Set up an integral for both orders of integration, and use the more convenient order to evaluate the integral below over the region R.
Ryx2+y2dA\iint _ { R } \frac { y } { x ^ { 2 } + y ^ { 2 } } d A
RR : triangle bounded by y=2x,y=6xy = 2 x , y = 6 x , and x=5x = 5


A) 5(log(37) log(5) ) 5 ( \log ( 37 ) - \log ( 5 ) )
B) 25(log(37) log(5) ) \frac { 2 } { 5 } ( \log ( 37 ) - \log ( 5 ) )
C) 52(log(37) log(5) ) \frac { 5 } { 2 } ( \log ( 37 ) - \log ( 5 ) )
D) 52(log(5) log(37) ) \frac { 5 } { 2 } ( \log ( 5 ) - \log ( 37 ) )
E) 13(log(37) log(5) ) \frac { 1 } { 3 } ( \log ( 37 ) - \log ( 5 ) )

Correct Answer:

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