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Differentiate w.r.t. θ
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\int \frac{1}{2}\times 2\sin(2\theta )\mathrm{d}x
Evaluate the indefinite integral first.
\frac{1}{2}\times 2x\sin(2\theta )
Find the integral of \frac{1}{2}\times 2\sin(2\theta ) using the table of common integrals rule \int a\mathrm{d}x=ax.
2\sin(\theta )\cos(\theta )+0\times 2\sin(\theta )\cos(\theta )
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.
\sin(2\theta )
Simplify.