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If \[F'(x)=f(x)\], which expression gives the indefinite integral of \[f(x)\]?

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Question

If \[F'(x)=f(x)\], which expression gives the indefinite integral of \[f(x)\]?

Options

  • \[\int f(x)\,dx=F(x)+C\]

  • \[\int f(x)\,dx=C\]

  • \[\int f(x)\,dx=F'(x)+C\]

  • \[\int f(x)\,dx=f'(x)+C\]

MCQ
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Solution

When \[F'(x)=f(x)\], \[F(x)\] is an anti-derivative of \[f(x)\]. All such anti-derivatives are represented by \[F(x)+C\].

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