Finding integral bounds

Question

i have this integral shown below is equal to 1, and i need to find "a" on mathematica, but I'm not sure how.

integral (from 0 to a) sqrt((-50.8938 sin(8.4823 t))^2+(4-11.3097 sin(11.3097 t))^2) dt = 1

any suggestions?

If you are asking a question about Mathematica why don't you write your code in a Mathematica-friendly way? — Öskå, Jun 19 '14 at 13:54
Start with the free-form input, see closely related: Symbolic Definite Integration — Artes, Jun 19 '14 at 15:03

score 5 · Accepted Answer · answered Jun 19 '14 at 14:52

f[t_?NumericQ] = 
  Sqrt[(-50.8938 Sin[8.4823 t])^2 + (4 - 11.3097 Sin[11.3097 t])^2];

Looking at a plot of f[t] to find an initial value for t in FindRoot

Plot[f[t], {t, 0, .1}]

enter image description here

Clear[a]

a = a /. FindRoot[
    NIntegrate[f[t], {t, 0, a}] == 1, {a, 0.08}] //
  Quiet

0.0680318

Check

NIntegrate[f[t], {t, 0, a}]

1.

Show[
 RegionPlot[0 <= t <= a && y <= f[t],
  {t, 0, .1}, {y, 0, 40},
  PlotPoints -> 50,
  AspectRatio -> 1/GoldenRatio],
 Plot[f[t], {t, 0, .1}]]

enter image description here

1 Answers1