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Create a plottable function using the Integrate[] Function?

Posted 13 days ago
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Hi;

I am having difficulty creating a plottable user function using the Integrate[] function - please see attached. Given, I am using the Integrate[] function to create an antiderivative with one variable and assuming that the constant is 0 in my attachment. However, once the user function is created,(F[x]) in my example, I cannot plug in a value for x or plot the function without errors and unexpected results.

Ideally, I would like to use antiderivatives much like derivatives by defining f[x] as a user function and f'[x] as the derivative and thus plotting them using Plot[{f[x],f'[x]},{x,-3,3}], which I really cannot seem to accomplish with antiderivatives.

In other words, I don't have a problem calculating the antiderivative using Mathematica's Integrate function, but am having trouble using the results. I know my problem is due to my lack of understanding so please help me understand what I am doing incorrectly.

Thanks,

Mitch Sandlin

Attachments:

Have a look at

f[x_] := x + 7
Plot[(Integrate[f[xx], xx]) /. xx -> x, {x, -3, 3}]
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