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'''4.7''' | '''4.7''' | ||
| − | Let <math>f</math> be a continuous function on <math>I = [-1, 1]</math> with the property that <math>int_{I} x^n f(x) \ dx = 0</math> for <math>n = 0, 1, ...</math>. Show that <math>f</math> is identically 0. | + | Let <math>f</math> be a continuous function on <math>I = [-1, 1]</math> with the property that <math>\int_{I} x^n f(x) \ dx = 0</math> for <math>n = 0, 1, ...</math>. Show that <math>f</math> is identically 0. |
'''Proof''' | '''Proof''' | ||
In progress | In progress | ||
Revision as of 17:11, 5 July 2009
4.7
Let $ f $ be a continuous function on $ I = [-1, 1] $ with the property that $ \int_{I} x^n f(x) \ dx = 0 $ for $ n = 0, 1, ... $. Show that $ f $ is identically 0.
Proof
In progress
