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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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∫  [f(x)  g′′  (x)  −  f′′  (x)  g  (x)]  dx\int \,\,\left[ {f\left( x \right)\,\,\mathrm{g''}\,\,\left( x \right)\,\, - \,\,f''\,\,\left( x \right)\,\,\mathrm{g}\,\,\left( x \right)} \right]\,\,dx is equal to
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Correct option: C
f(x)g′  (x)  −  f′  (x)  g  (x)f\left( x \right)\mathrm{g'}\,\,\left( x \right)\,\, - \,\,f'\,\,\left( x \right)\,\,\mathrm{g}\,\,\left( x \right)
Option C (f(x)g′ (x) − f′ (x) g (x)f(x)\mathrm{g'}\,(x)\, - \,f'\,(x)\,\mathrm{g}\,(x)) is correct because the integral simplifies to this expression after applying integration by parts twice.

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