- Thread starter shahar
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Please clarify what your question means. Are you asking about theIsIntegrala function?

Why yes? Why not?

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Please clarify what your question means. Are you asking about thedefinite integralof a function being a function (of the limits of integration?), or aboutan indefinite integral(an antiderivative) being a function, or perhaps aboutintegrationbeing an operator that takes a function to a new function (indefinite) or to a number (definite), or something else entirely?

To shahar: as put this is aIs Integral a function? Why yes? Why not?

I will say that

Now Leonard Gillman defined for \(\displaystyle x > 0,\quad L(x) = \int_1^x {\frac{1}{t}dt}\) for the so-called natural logarithm.

We look forward to your reply.

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Consider the function:What isone-parameter function?

\(\displaystyle f(x)=2x\)

Hence:

\(\displaystyle \int f(x)\,dx=x^2+C\)

This (on the RHS) is a one-parameter family of functions. The constant of integration is the parameter, and this anti-derivative is a family of functions where the parameter \(C\) can be any real number.