Evaluate
\frac{\pi ^{2}}{2}\approx 4.934802201
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\int \theta \mathrm{d}\theta
Evaluate the indefinite integral first.
\frac{\theta ^{2}}{2}
Since \int \theta ^{k}\mathrm{d}\theta =\frac{\theta ^{k+1}}{k+1} for k\neq -1, replace \int \theta \mathrm{d}\theta with \frac{\theta ^{2}}{2}.
\frac{\pi ^{2}}{2}-\frac{0^{2}}{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.
\frac{\pi ^{2}}{2}
Simplify.
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