$\int[f(x)g''(x)-f''(x)g(x)]dx$ is equal

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Indefinite Integration

Question:

$\int[f(x)g''(x)-f''(x)g(x)]dx$ is equal to:

Options:

$\frac{f(x)}{g'(x)}$

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

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

$f(x)g'(x)+f'(x)g(x)$

Correct Answer:

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

Explanation:

$\int[f(x)g''(x)-f''(x)g(x)]dx=\int f(x)g''(x)dx-\int f''(x)g(x)dx$

$=(f(x)g'(x)-\int f'(x)g'(x)dx)-(g(x)f'(x)-\int g'(x)f'(x)dx)=f(x)g'(x)-f'(x)g(x)$