Find the length of the spiraling polar curve r8e5theta From

Solution

For easiness I will write t instead of

The length element of a polar curve
r=f(t) is

sqrt(f²(t)+f\'²(t))

So we have

_0..2 sqrt(8^2*e^10t+8^2*25*e^10t) dt

=_0..28 e^5t 26 dt

=826e^5t/5|_0..2=

=826/5(e¹⁰-1)