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Simple Improper Integral Question (just a question of concept understanding)

  • Thread starter neden
  • Start date
  • #1
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Homework Statement



I am to determine whether the following integral is convergent or divergent

[tex]
\int_0^1 \frac{sin(x)}{x}
[/tex]

From what I hear since, lower limit is zero there is a removable discontinuity.
Thus just because of this, it is convergent? Can someone let me know if this
is correct.
 
Last edited:

Answers and Replies

  • #2
240
2
Do you know that:

[tex]lim(x->0) \frac{sin(x)}{x}=1[/tex]

?

If yes, then you can see that the function is bounded on the interval and therefore integrable.
 
  • #3
18
0
Oh thanks!
 

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