Evaluate
\sin(\pi n)
Differentiate w.r.t. n
\pi \cos(\pi n)
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\int _{0}^{1}\sin(n\pi )\mathrm{d}x
Cancel out 2 and 2.
\int \sin(n\pi )\mathrm{d}x
Evaluate the indefinite integral first.
\sin(n\pi )x
Find the integral of \sin(n\pi ) using the table of common integrals rule \int a\mathrm{d}x=ax.
\sin(\pi n)+0\sin(\pi n)
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(\pi n)
Simplify.
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