Evaluate
-\frac{4}{3}\approx -1.333333333
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\int x^{2}-2\mathrm{d}x
Evaluate the indefinite integral first.
\int x^{2}\mathrm{d}x+\int -2\mathrm{d}x
Integrate the sum term by term.
\frac{x^{3}}{3}+\int -2\mathrm{d}x
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{x^{3}}{3}-2x
Find the integral of -2 using the table of common integrals rule \int a\mathrm{d}x=ax.
\frac{2^{3}}{3}-2\times 2-\left(\frac{0^{3}}{3}-2\times 0\right)
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{4}{3}
Simplify.
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