# Finding integral bounds

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

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}]


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}]]