The discussion focuses on finding the arc length function for the curve defined by the equation \(y=2x^{3/2}\) starting from the point \(P_{0}(1,2)\). The derivative of the function is calculated as \(y'=3\sqrt{x}\), leading to the integral \(\int_{1}^{b} \sqrt{9x+1}\,dx\) for arc length. The starting point \(a\) is confirmed as 1, while the endpoint \(b\) remains variable, allowing the arc length to be expressed as a function of \(b\).
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ineedhelpnow said:find the arc length function for the curve $y=2x^{3/2}$ with starting point $P_{0}(1,2)$. how do i do this? this is what I've done so far.
$y'=3\sqrt{x}$
$1+(3\sqrt{x})^2=9x+1$
$\int_{a}^{b} \ \sqrt{9x+1}\,dx$
what's my a and what's my b?
ineedhelpnow said:ooookay! thanks! so i do it from 1 to x?