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

1. Mar 1, 2010

### neden

1. The problem statement, all variables and given/known data

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.

Last edited: Mar 1, 2010
2. Mar 1, 2010

### 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.

3. Mar 1, 2010

Oh thanks!