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