Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

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?

share|improve this question
1  
If you are asking a question about Mathematica why don't you write your code in a Mathematica-friendly way? –  Öskå Jun 19 at 13:54
1  
Start with the free-form input, see closely related: Symbolic Definite Integration –  Artes Jun 19 at 15:03
add comment

1 Answer 1

up vote 4 down vote accepted
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

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.