Evaluate
-3960
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\int _{0}^{2}220x-2200\mathrm{d}x
Use the distributive property to multiply 220 by x-10.
\int 220x-2200\mathrm{d}x
Evaluate the indefinite integral first.
\int 220x\mathrm{d}x+\int -2200\mathrm{d}x
Integrate the sum term by term.
220\int x\mathrm{d}x+\int -2200\mathrm{d}x
Factor out the constant in each of the terms.
110x^{2}+\int -2200\mathrm{d}x
Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x\mathrm{d}x with \frac{x^{2}}{2}. Multiply 220 times \frac{x^{2}}{2}.
110x^{2}-2200x
Find the integral of -2200 using the table of common integrals rule \int a\mathrm{d}x=ax.
110\times 2^{2}-2200\times 2-\left(110\times 0^{2}-2200\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.
-3960
Simplify.
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