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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


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