Evaluate
\frac{5}{3}\approx 1.666666667
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\int 5x^{2}\mathrm{d}x
Evaluate the indefinite integral first.
5\int x^{2}\mathrm{d}x
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\frac{5x^{3}}{3}
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}.
\frac{5}{3}\times 1^{3}-\frac{5}{3}\times 0^{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{5}{3}
Simplify.
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