New in Wolfram Mathematica 7: Integer Sequence Analysis ◄ previous | next ►
Determine Formulas for Definite Integrals
Find a formula for a definite integral for a parameter n.
In[1]:=

Click for copyable input
Table[\!\(

\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2\ \[Pi]\)]\(

SuperscriptBox[\(Sin[x]\), \(n\)] \[DifferentialD]x\)\), {n, 10}]
Out[1]=



In[2]:=

Click for copyable input
Table[\!\(

\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2\ \[Pi]\)]\(

SuperscriptBox[\(Sin[x]\), \(n\)] \[DifferentialD]x\)\), {n, 10}];

FindSequenceFunction[%, n]
Out[2]=



In[3]:=

Click for copyable input
Integrate[Sin[x]^n, {x, 0, 2 \[Pi]}, Assumptions -> n >= 0]
Out[3]=