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