There are lots of things going on at Wolfram Research these days. October 22–24 is our annual International Mathematica User Conference, and October 21 is the first-ever Wolfram|Alpha Homework Day! Homework Day is a groundbreaking, marathon live interactive web event that brings together students, parents, and educators from across the United States to solve their toughest assignments and explore the power of using Wolfram|Alpha for school, college, and beyond. You can read more about it in the Wolfram|Alpha Blog post.
Mathematica and Wolfram|Alpha are great resources for both teachers and students. Using the two together is a good way to explore topics in more depth. This video shows a few examples of how you can utilize Mathematica and Wolfram|Alpha in your own classroom.
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
Posted by Heis WernerbergOctober 19, 2009 at 7:04 pm