Find F (x) from the given F'(x)
F'(x) = 2 sin 5x + 3 cos (x/2) which is zero for $x = π / 3$

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Solution

$F^{'} (x) = 2 sin 5 x + 3 cos \frac{x}{2}$
$\int F^{'} (x) d x = - \frac{2 cos 5 x}{5} + 6 sin \frac{x}{2} + c = F (x)$
Given $F (\frac{π}{3}) = 0$
$F (\frac{π}{3}) = - \frac{1}{5} + 3 + c = 0$
$c = - \frac{14}{3}$
$F (x) = - \frac{2 cos 5 x}{5} + 6 sin \frac{x}{2} - \frac{14}{3}$

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