Suppose we have an integral of the form $$I = \int_a^b dx \, \sin(px), \tag{1}$$ where I've take $f(x;p) = \sin (px)$ to be specific. I want to plot this integral for a range of values of the parameter $10<p<100$ say. How can one do that? Please notice that the function $f$ is in reality kind of complicated and the integral must be done using numerical integration.
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asked Jun 8, 2015 at 14:39
1 Answer
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Define:
integ[p_?NumericQ] := NIntegrate[f[x, p], {x, a, b}]
Then plot it:
Plot[integ[p],{p,10,100}]
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$\begingroup$ Hey @Ivan, what if $p$ is a not a integer? Can we do the same but with smaller step-sizes, say 0.01? $\endgroup$ Jun 8, 2015 at 16:24
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$\begingroup$ @Love, nothing Ivan did here assumes that
pis an integer. He did forget the safety mechanism ofinteg[p_?NumericQ] := (* stuff*)tho. $\endgroup$ Jun 8, 2015 at 16:55 -
$\begingroup$ OK I assumed
integ[]had something to do with integers. $\endgroup$ Jun 8, 2015 at 16:56 -
$\begingroup$ Ops, just noticed that integ is just a name haha sorry $\endgroup$ Jun 8, 2015 at 16:58
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FunctionInterpolation[]for the purpose. $\endgroup$ListPlot[ NIntegrate[f[x,#],{x,a,b}]&/@Range[10,100] ]$\endgroup$f[{x,p}]:= Sin[p*x](say) and then writeListPlot[ NIntegrate[f[x,#],{x,a,b}]&/@Range[10,100] ]? $\endgroup$f[x_,p_]and when you use it. Either one works, but your definition would make me think that x and p typically come together in a list. $\endgroup$#means with respect to the second variable because it appears in the second position in the argument off? Now I've managed to plot my function actually but I want to be sure what it is I've plotted, i.e. if it is wrt to the "second-position" variable (I mean there are no other variables around so it must be but anyway). $\endgroup$