`y = 3/2 x^(2/3) , [1, 8]` Find the arc length of the graph of the function over the indicated interval.

Expert Answers

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Arc length (L) of the function y=f(x) on the interval [a,b] is given by the formula,

 `L=int_a^bsqrt(1+(dy/dx)^2)` dx, if y=f(x) and  a `<=`  x `<=`  b,

Now let's differentiate the function,




Now let's plug the derivative in the arc length formula,





 Now let's evaluate first the indefinite integral by using integral substitution,

Let `t=x^(2/3)+1`














Arc length (L) of the function over the given interval is `~~8.352`


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