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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
If ∫g(x)dx=g(x)\int g(x) d x=g(x), then ∫g(x)(f(x)−f′′(x))dx\int g(x)\left(f(x)-f^{\prime \prime}(x)\right) d x is equal to
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Correct option: B
g(x)(f(x)−f′(x))+cg(x)\left(f(x)-f^{\prime}(x)\right)+c
Option B (g(x)(f(x)−f′(x))+cg(x)(f(x)-f^{\prime}(x))+c) is correct because integrating by parts and using the given condition ∫g(x)dx=g(x)\int g(x) dx = g(x) simplifies the expression to this result.

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