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Using Mathematica and Wolfram|Alpha in the Classroom
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