Comments on: Using Mathematica and Wolfram|Alpha in the Classroom http://blog.wolfram.com/2009/10/19/using-mathematica-and-wolframalpha-in-the-classroom/ News, views, & ideas from the front lines at Wolfram Research Fri, 10 Feb 2012 12:21:10 -0600 http://wordpress.org/?v=2.8.4 hourly 1 By: Heis Wernerberg http://blog.wolfram.com/2009/10/19/using-mathematica-and-wolframalpha-in-the-classroom/comment-page-1/#comment-1211 Heis Wernerberg Tue, 20 Oct 2009 00:04:24 +0000 http://blog.internal.wolfram.com/?p=2020#comment-1211 In the video, at 1 min 26 s, the integral shown is int_7.34^3tanx dx = 1.48164 This is wrong! The function tan(x) has a nonintegrable singularity at 3/2Pi ~~ 4.712 inside the integration interval. And even if you consider the integral in a Cauchy sense (you would not tell students about principal values and finite parts anyway), the result is wrong. Compare with the result of Mathematica for this integral: In[1]:= Integrate[Tan[x], {x, 7.34, 3}] Out[1]= -1.12812 + 0. I In[2]:= Integrate[Tan[x], {x, 7.34, 3}, PrincipalValue -> True] Out[2]= -0.699934 + 0. I In[3]:= NIntegrate[Tan[x], {x, 7.34, 3}] Out[3]= 0. In[4]:= NIntegrate[Tan[x], {x, 7.34, 3 Pi/2, 3}, Method -> "PrincipalValue"] Out[4]= -0.699934 In the video, at 1 min 26 s, the integral shown is

int_7.34^3tanx dx = 1.48164

This is wrong! The function tan(x) has a nonintegrable singularity at 3/2Pi ~~ 4.712 inside the integration interval.

And even if you consider the integral in a Cauchy sense (you would not tell students about principal values and finite parts anyway), the result is wrong. Compare with the result of Mathematica for this integral:

In[1]:= Integrate[Tan[x], {x, 7.34, 3}]

Out[1]= -1.12812 + 0. I

In[2]:= Integrate[Tan[x], {x, 7.34, 3},
PrincipalValue -> True]

Out[2]= -0.699934 + 0. I

In[3]:= NIntegrate[Tan[x], {x, 7.34, 3}]

Out[3]= 0.

In[4]:= NIntegrate[Tan[x], {x, 7.34, 3 Pi/2, 3},
Method -> “PrincipalValue”]

Out[4]= -0.699934

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