Mathematics

Mathematics

Problem

For a smooth curve given by y=f(x)y=f(x) with f′(x)f'(x) continuous on [a,b][a,b], which expression represents an infinitesimal element of arc length along the curve? a) ds=1+(dxdy)2 dxds=\sqrt{1+\left(\dfrac{dx}{dy}\right)^2}\,dx b) ds=(1+(dydx)2) dxds=\bigl(1+\left(\dfrac{dy}{dx}\right)^2\bigr)\,dx c) ds=1+(dydx)2 dxds=\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}\,dx d) ds=∣dydx∣ dxds=\left|\dfrac{dy}{dx}\right|\,dx

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