Arc Length of a Curve

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The arc length, $L$ ,along the curve $y = f (x)$ from $x = a$ to $x = b$ is given by $(L = \int_{a}^{b} \sqrt{1 + f^{'} (x)^{2}} d x$

The arc length, $L$ ,along the curve $x = g (y)$ from $y = c$ to $x = d$ is given by $L = \int_{c}^{d} \sqrt{1 + g^{'} (y)^{2}} d y$