`x = 1/3sqrt(y)(y-3) , 1<=y<=4` Find the arc length of the graph of the function over the indicated interval.

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Arc length (L) of the function x=h(y) on the interval [c,d] is given by the formula,

`L=int_c^dsqrt(1+(dx/dy)^2)dy`  , if x=h(y) and c `<=`  y `<=`  d,

Now let's differentiate the function with respect to y,









Plug in the above derivative in the arc length formula,







Now let's compute first the indefinite integral by applying integral substitution,

Let `u=sqrt(y)`






substitute back u= `sqrt(y)`  and add a constant C to the solution,









Arc length of the function over the given interval is `10/3`

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