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

[neden]

Homework Statement

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

$$\int_0^1 \frac{sin(x)}{x}$$

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.

 

[elibj123]

Do you know that:

$$lim(x->0) \frac{sin(x)}{x}=1$$

?

If yes, then you can see that the function is bounded on the interval and therefore integrable.

 

[neden]

Oh thanks!