Evaluate
\frac{\sqrt{2}\left(\sqrt{2}\sin(4)+1\right)}{2}\approx -0.049695714
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\int \cos(x)\mathrm{d}x
Evaluate the indefinite integral first.
\sin(x)
Use \int \cos(x)\mathrm{d}x=\sin(x) from the table of common integrals to obtain the result.
\sin(4)-\sin(-\frac{\pi }{4})
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(4)+\frac{\sqrt{2}}{2}
Simplify.
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