We'll evaluate the indefinite integral of the given
function to determine the antiderivative.
We'll re-write
the given function using the double angle identity:
y =
2sin 2x*cos 2x/2
y = sin
(4x)/2
sin 2x*cos 2x dx =
sin (4x)
dx/2
Let 4x = t => 4dx = dt => dx =
dt/4
sin (4x) dx/2 =
sin t
dt/8
sin t dt/8 = - cos t/8 +
C
sin 2x*cos 2x dx = - cos (4x)/8 +
C
The antiderivative of the given function is
the original function Y = - cos (4x)/8 + C.
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