Evaluate
4\left(1-\cos(4)\right)\approx 6.614574483
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\int 4\sin(x)\mathrm{d}x
Evaluate the indefinite integral first.
4\int \sin(x)\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
-4\cos(x)
Use \int \sin(x)\mathrm{d}x=-\cos(x) from the table of common integrals to obtain the result.
-4\cos(4)+4\cos(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.
4\left(-\cos(4)+1\right)
Simplify.
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