can be rewritten as
Notice that the functions sin6(x) and cos6(x) have the same integrals on the intervals 0 to pi/2, so
,
therefore 
.The last integral is pi/2, but since you have to divide it by 2, the final answer is pi/4 or 0.785.
Solution
The integral
can be rewritten as
Notice that the functions sin6(x) and
cos6(x) have the same integrals on the
intervals 0 to pi/2, so
,
therefore .
The last integral is pi/2, but since you have to divide it by 2,
the final answer is pi/4 or
0.785.