Confusion in Numerical Integration while using FindRoot

I used this code for numerical integration

NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, 13}]


when upperlimit of x is 13, the integral value is 50.

Now I want to find the upper-limit of this integration where integration value is known i.e. 50. I write the follwing code

PL = NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, v}];
FindRoot[PL == 50, {v, 11}]


But this code is not giving me the correct value of v. Even when i change {v,11} to {v,10} or {v,7}, it shows different values of v. I plotted PL as a function of v from 0 to 14. But when I agian crosscheck using the ouput as upperlimit of numerical integration I do not get back 50.

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You can also use Solve

Solve[Integrate[
(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x],
{x, 1.414, v}] == 50, v, Reals][[1]] // Quiet


{v -> 12.9905}

s[v_?NumericQ] := NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, v}]
FindRoot[s[v] == 50, {v, 11}]
(* {v -> 12.9905} *)

• But when you change {v,11} to {v,1}, it gives different value – Abhijit Saha Mar 25 '15 at 4:43
• Is there any way to do this without defining a new function? – Louis Yang Jan 17 '17 at 20:59