Question

菜鸟！急问！求助一个Mathematica做积分的问题！

程序如下：
In[1]:=6*1.1^3*NIntegrate[
Exp[-0.03*(s + x + v) - 0.002*(x^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*x^2 + 6*x^3 - 12*x*v^2 + 17*v^3)], {v, 0,
1000}, {x, v, 1000}, {s, x, 1000}] -
6*3*1.1^2*
NIntegrate[
Exp[-0.03*(s + x + v) - 0.002*(x^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*x^2 + 6*x^3 - 12*x*v^2 + 17*v^3)], {v, 0,
1000}, {x, v, 1000}, {s, x, 1000}] +
2*3*1.1*NIntegrate[
Exp[-0.03*(s + 2*v) - 0.002*(s^2 + 2*v^2)/2 +
0.001^2/6*(17*s^3 + 12*v*s^2 + 4*v^3)], {v, 0, 1000}, {s, 0,
v}] + 2*3*1.1*
NIntegrate[
Exp[-0.03*(s + 2*v) - 0.002*(s^2 + 2*v^2)/2 +
0.001^2/6*(s^3 - 3*s*v^2 + 11*v^3)], {v, 0, 1000}, {s, v,
1000}] +
6*3*1.1*NIntegrate[
Exp[-0.03*(s + u + v) - 0.002*(u^2 + s^2 + v^2)/2 +
0.001^2/6*(s^3 - 3*s*u^2 + 6*u^3 - 12*u*v^2 + 17*v^3)], {v, 0,
1000}, {u, v, 1000}, {s, u, 1000}] - 6682.90

出来如下的结果：NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >>
General::stop: Further output of NIntegrate::slwcon will be suppressed during this calculation. >>
Out[1]=2.704725569675203*10^1045

Ps.上面是积分限取1000的结果，积分限取800的时候等于1.321678837009696*10^357
可是积分的指数函数应该是收敛的。。。怎么会越来越大了呢？

Answer 1

有奇点或者被积函数小于零，所以发散了哦。积分上限取800时出来的结果也是错的。你可以先把被积函数画出来，看是不是有奇点，然后可以分段积分，跳过奇点。