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Determine Formulas for Definite Integrals
Find a formula for a definite integral for a parameter n.
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Table[\!\(

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

SuperscriptBox[\(Sin[x]\), \(n\)] \[DifferentialD]x\)\), {n, 10}]
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In[2]:=

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Table[\!\(

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

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

FindSequenceFunction[%, n]
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In[3]:=

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Integrate[Sin[x]^n, {x, 0, 2 \[Pi]}, Assumptions -> n >= 0]
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