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Question Number 201463 by hardmath last updated on 06/Dec/23

$$\mathrm{a}=\mathrm{constant}\mathrm{number}:$$$$\mathrm{if}\int \mathrm{x}\cdot \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}={\mathrm{x}}^3-{\mathrm{x}}^2+4\mathrm{x}-\frac{\mathrm{a}}{5}$$$$\mathrm{find}\mathrm{f}\left(2\right)=?$$

Answered by mr W last updated on 06/Dec/23

$$definition:$$$$\int g\left(x\right)dx=G\left(x\right)means$$$$g\left(x\right)=\frac{dG\left(x\right)}{dx}$$$$$$$$xf\left(x\right)=\frac{d}{dx}(x^3-x^2+4x-\frac{a}{5})$$$$xf\left(x\right)=3x^2-2x+4$$$$\Rightarrow f\left(x\right)=3x-2+\frac{4}{x}$$$$\Rightarrow f\left(2\right)=3\times 2-2+\frac{4}{2}=6✓$$

Commented by hardmath last updated on 08/Dec/23

$$\mathrm{cool}\mathrm{dear}\mathrm{professor}\mathrm{thank}\mathrm{you}$$

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