Evaluate
\frac{\pi ^{3}}{3}\approx 10.33542556
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\int t^{2}\mathrm{d}t
Evaluate the indefinite integral first.
\frac{t^{3}}{3}
Since \int t^{k}\mathrm{d}t=\frac{t^{k+1}}{k+1} for k\neq -1, replace \int t^{2}\mathrm{d}t with \frac{t^{3}}{3}.
\frac{\pi ^{3}}{3}-\frac{0^{3}}{3}
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 ^{3}}{3}
Simplify.
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