Arclength Calculation Process for y=x^3/2, 0<x<5/9

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jnimagine
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this is a really easy question... but seems like i keep getting something wrong in my calculations... - -
Find the arclength of y = x^3/2 0<x<5/9
when i do it using the formula; L = sqreroot (1+(dx/dy)^2)
i keep getting one...
can someone post the calculation process...
 
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jnimagine said:
can someone post the calculation process...

Yes...you can:wink:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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