How does one use NSum within NIntegrate properly?

Question

If I use symbolic integration for the following:

Sum[Integrate[i + x, {x, 1, 7}], {i, 1, 7}]

336

as one can see it gives the answer as it seems to 'understand' the sum integral.

However with

NSum[NIntegrate[i + x, {x, 1, 7}], {i, 1, 7}]

NIntegrate::inumr: The integrand i+x has evaluated to non-numerical values for all sampling points in the region with boundaries {{1,7}}.

336.

As one can see it does not seem to know that $i$ is 1 I think or something like that.

What is the problem and how can I format the numerical functions to do what I want without these errors?

Use Quiet[] or ignore it. NSum[] is evaluating its argument symbolically probably to see if it can be differentiated — Michael E2, Jun 24 '19 at 22:09
Possible duplicate: https://mathematica.stackexchange.com/questions/18393/what-are-the-most-common-pitfalls-awaiting-new-users/26037#26037 — Michael E2, Feb 07 '21 at 02:57
Michael E2 Jun 24 '19 at 22:09 then Michael E2 yesterday Feb 07 '21 just noticed aye! — onepound, Feb 08 '21 at 12:58

score 2 · Accepted Answer · answered Jun 24 '19 at 19:30

2

Define a function that can only be called with a numerical argument $i$:

f[i_?NumericQ] := NIntegrate[i + x, {x, 1, 7}]

Numerical sum without possibility of analytic attempts at integration:

NSum[f[i], {i, 1, 7}]
(*    336.    *)

answered Jun 24 '19 at 19:30

Roman

1 Answers1