_ ^ [f(x) ,g''(x) - f''(x) ,g(x)] ,dx = - Vidyadip

MCQ

$\int_{}^{} {[f(x)\,g''(x) - f''(x)\,g(x)]\,dx} $=

A
$\frac{{f(x)}}{{g'(x)}}$
B
$f'(x)g(x) - f(x)g'(x)$
✓
$f(x)g'(x) - f'(x)g(x)$
D
$f(x)g'(x) + f'(x)g(x)$

✓

Answer

Correct option: C.

$f(x)g'(x) - f'(x)g(x)$

c
(c)$\int_{}^{} {[f(x)\,g''(x) - f''(x)\,g(x)]\,dx} $
$ = \int_{}^{} {f(x)\,g''(x)\,dx} - \int_{}^{} {f''(x)\,g(x)\,dx} $
$ = \left( {f(x)\,g'(x) - \int_{}^{} {f'(x)g'(x)\,dx} } \right) - \left( {g(x)\,f'(x) - \int_{}^{} {g'(x)\,f'(x)\,dx} } \right)$
$ = f(x)\,g'(x) - f'(x)\,g(x).$

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