Evaluate
\frac{56}{3}\approx 18.666666667
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\int y^{2}\mathrm{d}y
Evaluate the indefinite integral first.
\frac{y^{3}}{3}
Since \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} for k\neq -1, replace \int y^{2}\mathrm{d}y with \frac{y^{3}}{3}.
\frac{4^{3}}{3}-\frac{2^{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{56}{3}
Simplify.
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