Evaluate
\frac{\pi ^{2}}{2}\approx 4.934802201
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\int _{0}^{\pi }x\mathrm{d}x
Anything divided by one gives itself.
\int x\mathrm{d}x
Evaluate the indefinite integral first.
\frac{x^{2}}{2}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{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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