integral from -pi/2 to pi/2 cos^56x dx does this = 0?

Answer 1

Hi!
(cos(x))^56 is always a non negative number.
So Its integral over any (non point) region must always be greater than 0.

Answer 2

int. cos^56 x dx eh?
Why don't we aim for something even more general,
by de Moivre's theorem,
z^n = (cos z + isin z)^n = cos nz + isin nz

Also z^-n =(cos z + isin z)^-n = cos nz - isin nz
then,
for any n, 2cos nz = (z + 1/z)^n
Now derive an expression for cos^n z for odd and even cases and integrate in the given limits.(you can get a general form for the integral if you denote your result by a finite sum!

Hope this helps!!