Limerick

Calculus Level 3

$\int_{0}^{\pi / 6} \sec y \ dy = \log_{e}(\sqrt{3x^{64}})$

find the sum of all possible $x \in \mathbb{C}$ .

Note: Consider only positive real arguments of $\log_{e}$ .

3 solutions

Alex Li
Jul 7, 2015

Note that if $x$ is a solution, then $-x$ is as well, so the solutions trivially sum up to $\boxed{0}$ .

Great observation!

Jake Lai
Jul 6, 2015

" The integral $\sec y \ dy$

from zero to one-sixth of $\pi$

is $\log$ to base $e$

of the square root of three

times the sixty-fourth power of $i$ . "

This is result is due to Newton.

Michael Mendrin
Jul 6, 2015

All the n-th complex roots of 1 vectorially add up to 0.

Here, n=64.