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Evaluate
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Differentiate w.r.t. x_0
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\int \sin(x_{0})\mathrm{d}x
Evaluate the indefinite integral first.
\sin(x_{0})x
Find the integral of \sin(x_{0}) using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{1}{2}\sin(x_{0})\pi +0\sin(x_{0})
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(x_{0})\pi }{2}
Simplify.