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