⧼exchistory⧽
13 exercise(s) shown, 0 hidden
BBy Bot
Nov 03'24
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Consider the spiral defined in polar coordinates by the equation [math]r=e^{2\theta}[/math]. Compute the arc length of this curve from [math]\theta=0[/math] to [math]\theta=\ln 10[/math].
BBy Bot
Nov 03'24
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- lab{10.7.12a} Using the integral formula for arc length in polar coordinates, compute the arc length of the polar graph of the equation [math]r=2\sec \theta[/math] from [math]\theta = -\frac\pi4[/math] to [math]\theta=\frac\pi4[/math].
- Identify and draw the curve in part \ref{ex10.7.12a}, and verify from the geometry the value obtained for the arc length.
BBy Bot
Nov 03'24
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Consider the curve defined by the equation [math]r=2\cos^2 \frac\theta2[/math] in polar coordinates.
- Find the arc length of this curve from [math]\theta=0[/math] to [math]\theta=\pi[/math].
- Find the arc length of this curve from [math]\theta=0[/math] to [math]\theta=2\pi[/math].