Evaluate
\frac{\pi \omega \sin(2tw)}{2}
Differentiate w.r.t. w
\pi t\omega \cos(2tw)
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\int \sin(2wt)\mathrm{d}x
Evaluate the indefinite integral first.
\sin(2wt)x
Find the integral of \sin(2wt) using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{1}{2}\sin(2wt)\pi \omega +0\sin(2wt)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
\frac{\sin(2wt)\pi \omega }{2}
Simplify.
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