Tutorial Exercise Find the arc length function for the curve y=2x3/2 with starting point Po(16, 128). Step 1 Recall that for a smooth curve C given by the equation y = f(x) over the interval a sxs b, the arc length function is given by the following. Note that this is the usual formula for arc length, however the endpoint is replaced by the variable x rather than a fixed endpoint. As s is written as a function of x, we use t for the variable of integration to avoid confusion. We are asked to find the arc length function for the curve y = 2x3/2 with starting point Po(16, 128). First, we first need to find its derivative. dx y = 2x ³/2 3√x 3√

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