`x = 1/3(y^2 + 2)^(3/2) , 0<=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,




Plug in the above derivative in the arc length formula,











Arc length of the function over the given interval is `76/3`


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