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Question Number 78717 by jagoll last updated on 20/Jan/20

$$\mathrm{given}$$$$\int \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\frac{1}{2\sqrt[3]{\mathrm{g}\left(\mathrm{x}\right)}}.$$$${\mathrm{g}}^{\prime }\left(1\right)=\mathrm{g}\left(1\right)=8\Rightarrow \mathrm{f}\left(1\right)=?$$$$$$

Commented by john santu last updated on 20/Jan/20

$$\int f\left(x\right)dx=\frac{1}{2}{\left(g\left(x\right)\right)}^{-\frac{1}{3}}$$$$f\left(x\right)=-\frac{1}{6}{g}^{\prime }\left(x\right)\times \frac{1}{\sqrt[3]{{\left(g\left(x\right)\right)}^4}}$$$$f\left(1\right)=-\frac{1}{6}.\left(8\right).\frac{1}{16}=-\frac{1}{12}★$$

Commented by jagoll last updated on 20/Jan/20

$$\mathrm{thanks}$$

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