In[]:=
​​AsymptoticIntegrate
1
4
2
x
-1
Exp[-λ
2
Sin[πx]
],{x,1,∞},{λ,+∞,1}
Out[]=
1
λ
15
π
In[]:=
​​Exact[λ_]:=NIntegrate
1
4
2
x
-1
Exp[-λ
2
Sin[πx]
],{x,1,∞},PrecisionGoal10;​​Approx1[λ_]:=
1
λ
15
π
;​​Approx2[λ_]:=
1
3
1
πλ
;
In[]:=
Plot[{Exact[λ],Approx1[λ],Approx2[λ]},{λ,1,10}]
Out[]=