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How to plot an integral with variable limits?

James Bainbridge
Posted 5 years ago

I am trying to plot the following integral:

Integrate[1/2*(4*((1-v)*Exp[-2/5*t]-1)/((1-v)*Exp[-2/5*t]+1)^5-1)^2, {t, 0, 2/5*Log[99*(1-v)]}]

Against a range of v variables, {0.01,0.99,0.0098} but I keep getting the same error saying my limit of integration is not valid, is there another function I can use?
POSTED BY: James Bainbridge
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Updating Name
Updating Name
Posted 5 years ago

This has sorted it, thank you very much.
POSTED BY: Updating Name 
$Version
(*12.2.0 for Microsoft Windows (64-bit) (December 12, 2020)*)

 f[v_] := NIntegrate[
    1/2 (4 ((1 - v) Exp[-2/5 t] - 1)/((1 - v) Exp[-2/5 t] + 1)^5 - 
        1)^2, {t, 0, 2/5 Log[99 (1 - v)]}];(*With mumerics*)
  Plot[f[v], {v, 0.0098, 0.99}]

  g = Integrate[
    1/2 (4 ((1 - v) Exp[-2/5 t] - 1)/((1 - v) Exp[-2/5 t] + 1)^5 - 
        1)^2, {t, 0, 2/5 Log[99 (1 - v)]}, Assumptions -> v > 0](*Symbolic solution*)
  Plot[Evaluate[g[[1]]], {v, 0.0098, 0.99}]
POSTED BY: Mariusz Iwaniuk
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