Problem

\( \int_{0}^{3} x^{2}-3 x-9 \)

Answer

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Answer

\( \begin{split} \int_{0}^{3} x^{2}-3 x-9\,\mathrm{d}x = \left[ \frac{1}{3}x^3 - \frac{3}{2}x^2 - 9x \right]_0^3 \end{split}\)

Steps

Step 1 ：\( \int x^{2}-3 x-9\,\mathrm{d}x = \int x^2\,\mathrm{d}x - \int 3x\,\mathrm{d}x - \int 9\,\mathrm{d}x \)

Step 2 ：\( \int x^2\,\mathrm{d}x = \frac{1}{3}x^3 + C_1 \)

Step 3 ：\( \int 3x\,\mathrm{d}x = \frac{3}{2}x^2 + C_2 \)

Step 4 ：\( \int 9\,\mathrm{d}x = 9x + C_3 \)

Step 5 ：\( \int x^{2}-3 x-9\,\mathrm{d}x = \left( \frac{1}{3}x^3 - \frac{3}{2}x^2 - 9x \right) + C \)

Step 6 ：\( \begin{split} \int_{0}^{3} x^{2}-3 x-9\,\mathrm{d}x = \left[ \frac{1}{3}x^3 - \frac{3}{2}x^2 - 9x \right]_0^3 \end{split}\)

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