Re: Bug of Integrate
- To: mathgroup at smc.vnet.net
- Subject: [mg82721] Re: Bug of Integrate
- From: Bhuvanesh <lalu_bhatt at yahoo.com>
- Date: Tue, 30 Oct 2007 03:18:53 -0500 (EST)
Actually, the integral should have given zero. The integrand is not quite equal to 3 (taking the square root of x^2 does not give x).
In[1]:= PiecewiseExpand[Simplify[Sqrt[1/Cos[t]^2]*3*Cos[t], 0<t<2Pi], 0<t<2Pi]
Out[1]= Piecewise[{{-3, Sec[t] < 0}}, 3]
The wrong -6*Pi result was due to a wrong result from the following integral:
Integrate[UnitStep[Sec[t]], {t, 0, 2*Pi}]
This is already fixed in the development version:
In[1]:= Integrate[Sqrt[1/Cos[t]^2]*3*Cos[t], {t, 0, 2Pi}]
Out[1]= 0
In[2]:= NIntegrate[Sqrt[1/Cos[t]^2]*3*Cos[t], {t, 0, 2Pi}]
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::ncvb:
NIntegrate failed to converge to prescribed accuracy after 9
recursive bisections in t near {t} = {4.16006}. NIntegrate obtained
-15 -15
-3.23352 10 and 2.60898 10 for the integral and error estimates.
-15
Out[2]= -3.23352 10
Bhuvanesh,
Wolfram Research