# What is the arclength of #r=4theta # on #theta in [-pi/4,pi]#?

This is an outline method. The grind of some of the work has been done by computer.

Arc length

and

Now, for

So

Arc length

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The arc length of ( r = 4\theta ) on the interval ( \theta ) in ( [-\frac{\pi}{4}, \pi] ) is ( \frac{5\sqrt{2}}{2} + 4\pi ) units.

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