Evaluate
2\cos(\alpha )
Differentiate w.r.t. α
-2\sin(\alpha )
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\int \sin(x)\mathrm{d}x
Evaluate the indefinite integral first.
-\cos(x)
Use \int \sin(x)\mathrm{d}x=-\cos(x) from the table of common integrals to obtain the result.
-\cos(\pi +\alpha )+\cos(\alpha )
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.
2\cos(\alpha )
Simplify.
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