given-f-x-dx-1-2-g-x-1-3-g-1-g-1-8-f-1-

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

given

\int f (x) dx = \frac{1}{2 \sqrt[3]{g (x)}} .

g^{'} (1) = g (1) = 8 \Rightarrow f (1) = ?

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

\int f (x) d x = \frac{1}{2} {(g (x))}^{- \frac{1}{3}}

f (x) = - \frac{1}{6} g^{'} (x) \times \frac{1}{\sqrt[3]{{(g (x))}^{4}}}

f (1) = - \frac{1}{6} . (8) . \frac{1}{16} = - \frac{1}{12} ★

Commented by jagoll last updated on 20/Jan/20

thanks

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