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\int 24-4x\mathrm{d}x
Evaluate the indefinite integral first.
\int 24\mathrm{d}x+\int -4x\mathrm{d}x
Integrate the sum term by term.
\int 24\mathrm{d}x-4\int x\mathrm{d}x
Factor out the constant in each of the terms.
24x-4\int x\mathrm{d}x
Find the integral of 24 using the table of common integrals rule \int a\mathrm{d}x=ax.
24x-2x^{2}
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 -4 times \frac{x^{2}}{2}.
24\times 5-2\times 5^{2}-\left(24\times 0-2\times 0^{2}\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.
70
Simplify.
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