# Plot a double integral

I'm trying to plot the result of a double Integral

Plot[
Integrate[Integrate[x^7 (x - 2)^4 (x - 3)^9, x], x]
,{x, -10, 10}
]


Results in a 22-degree polynomial, but why doesn't the above Plot work?

Can you update the Answer to state/explain why x=2 is not the point of inflection but x=0,3 are?

• Use Evaluate or do p = Integrate[Integrate[x^7*(x - 2)^4*(x - 3)^9, x], x]; Plot[p, {x, -10, 10}] screen shot !Mathematica graphics Dec 3, 2021 at 5:50

Try this:

f[x_] = Integrate[Integrate[x^7 (x - 2)^4 (x - 3)^9, x], x]


Plot:

Plot[f[x], {x, 2, 4.1}, PlotRange -> All, AspectRatio -> 1/GoldenRatio]


• Thanks! Now why doesn't this function have a point of inflection at 2? (only 0 and 3). Could I have seen that just by looking at f" instead of plotting it? Even the 0 and 3 do not show from the plot, unless it's zoomed out a lot. Dec 3, 2021 at 6:09
• If you are going to make a function, you might consider making it immediate assignment instead of delayed, and then no need to do evaluate. As in f[x_] = Integrate[Integrate[x^7 (x - 2)^4 (x - 3)^9, x], x]; Plot[f[x], {x, -10, 10}, AspectRatio -> 1/GoldenRatio] Only first time it will automatically evaluate the integral, but future calls will not. Just another option. Both methods work the same way. Dec 3, 2021 at 6:11
• @E. Chan-López: See updated question plz Dec 3, 2021 at 16:14