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.