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Operations with negative sign 
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#1
Mar1814, 12:59 AM

P: 20

While working on an integration problem I found that I will arrive at two different solutions depending on how I approach it.
I'm finding the arc length of y=ln(1x^{2}) on the interval [0,0.5] The formula for finding the arc length is ∫sqrt[1+[f'(x)]^{2}]dx So f'(x) = 2x / ( 1x^{2} ) Here I first simplify this to 2x / ( x^{2}  1 ) and squaring gives 4x^{2} / ( x^{2} 1 )^{2} Working from here I end up integrating from 0 to 0.5 ∫ [1 + 1/(x1)  1/(x+1)] dx = 0.5  ln3 On the other hand if I leave f'(x) as it is without simplifying, when I squared f'(x) I get 4x^{2} / ( 1x^{2} )^{2} and end up integrating from 0 to 0.5 ∫ [1 + 1/(1+x) + 1/(1x)] dx = 0.5  ln3 Should both have the same solution or is this simply a possible effect from squaring numbers? Thank you 


#2
Mar1814, 03:47 AM

Sci Advisor
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P: 12,016

Note that when taking the square root of the perfect square in your denominator, you must use the ABSOLUTE value, x^21 as your new denominator.



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