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