in Calculus recategorized by
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1 vote
1 vote

Let $g:[0, \pi] \rightarrow \mathbb{R}$ be continuous and satisfy
\[
\int_{0}^{\pi} g(x) \sin (n x) d x=0
\]
for all integers $n \geq 2$. Then which of the following can you say about $g?$ 

  1. $g$ must be identically zero.
  2. $g(\pi / 2)=1$.
  3. $g$ need not be identically zero.
  4. $g(\pi)=0$.
  5. None of the above.
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