Evaluate

$0$

sin$2(2$x$)$ dx$.$

Solution

If we write

sin$2(2$x$)=1$ cos$2(2$x$),$

the integral is no simpler to evaluate. Using the half$-$angle formula for

sin$2($x$),$

however, we have

$0$

sin$2(2$x$)$ dx$=$

$12$

$0$

$(1$ cos$(4$x$))$ dx