1
$\begingroup$

I want to integrate this function with respect to θ1 and then take the derivative of that function with respect to n. Since the integral is not a known function I am having trouble with this operation. Does anyone have any ideas? I know that I can perform numerical integration on the function. The limits of integration that I'm interested in are 0 and ArcSin[0.2/n].

1/2 ((n Cos[θ1] - 
 0.2 Sqrt[1 - 25. n^2 Sin[θ1]^2])^2/(n Cos[θ1] + 
 0.2 Sqrt[1 - 25. n^2 Sin[θ1]^2])^2 + (-0.2 Cos[θ1] + 
 n Sqrt[1 - 25. n^2 Sin[θ1]^2])^2/(0.2 Cos[θ1] + 
 n Sqrt[1 - 25. n^2 Sin[θ1]^2])^2)
$\endgroup$
3
$\begingroup$

If numerical results are acceptable;

Needs["NumericalCalculus`"]

func[θ1_,n_]:= 1/2 ((n Cos[θ1] - 
 0.2 Sqrt[1 - 25. n^2 Sin[θ1]^2])^2/(n Cos[θ1] + 
 0.2 Sqrt[1 - 25. n^2 Sin[θ1]^2])^2 + (-0.2 Cos[θ1] + 
 n Sqrt[1 - 25. n^2 Sin[θ1]^2])^2/(0.2 Cos[θ1] + 
 n Sqrt[1 - 25. n^2 Sin[θ1]^2])^2)

int[n_?NumberQ] := 
 int[n] = NIntegrate[func[\[Theta]1, n], {\[Theta]1, 0, ArcSin[.2/n]},
    AccuracyGoal -> 10]
der[n0_?NumberQ] := der[n0] = ND[int[n], n, n0]

der[4]
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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