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\int 15x^{2}-12x\mathrm{d}x
Evaluate the indefinite integral first.
\int 15x^{2}\mathrm{d}x+\int -12x\mathrm{d}x
Integrate the sum term by term.
15\int x^{2}\mathrm{d}x-12\int x\mathrm{d}x
Factor out the constant in each of the terms.
5x^{3}-12\int x\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}. اضرب 15 في \frac{x^{3}}{3}.
5x^{3}-6x^{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}. اضرب -12 في \frac{x^{2}}{2}.
5\times 2^{3}-6\times 2^{2}-\left(5\times 1^{3}-6\times 1^{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.
17
تبسيط.