# Plotting multiple instances of a function defined with NIntegrate

I have a function that involves an NIntegrate, for example something like this:

f[x_, z_] := NIntegrate[z*x*y^2, {y, 0, x}];

I want to plot this function for a large number of different values of z, and all on the same graph. The naive attempt:

Plot[Evaluate@Table[f[x, t], {t, 1, 15}],{x, 30, 70}]

This gives the error

NIntegrate::nlim: y = x is not a valid limit of integration.

I’ve tried various combinations of hold and activate and inactivate, but haven’t stumbled upon anything that works. How can I do this?

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It returns the errors for me in Version 10.2 on Windows 8.1 64-bit, but still generates the plot. Taking out the Evaluate and just executing Plot[Table[f[x, t], {t, 1, 15}],{x, 30, 70}] returns the plot with no errors (although with a notably longer execution time).
– IPoiler
Sep 4 ’15 at 2:23

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– Michael E2
Sep 4 ’15 at 2:33

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1

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f[x_?NumericQ, z_?NumericQ] := NIntegrate[z*x*y^2, {y, 0, x}]
Plot[Evaluate@Table[f[x, t], {t, 1, 15}], {x, 30, 70}]

1

Of course you could get z out of the integral. I assume that’s because you posted a toy example
– Dr. belisarius
Sep 4 ’15 at 3:19