# Homework Help: Question about Integration

1. Jan 14, 2012

### GreenPrint

$\int^{b}_{a}$ f(x) dx = $lim_{c → a^{+}}$ $lim_{d → b^{-}}$ $\int^{d}_{c}$ f(x) dx

Is this true?

2. Jan 14, 2012

### HACR

What are the arguments of the limit in this case?

3. Jan 14, 2012

### GreenPrint

a and b on the left hand side and I replaced these with c and d evaluated with limits with a and b, a from the right and b from the left.

4. Jan 14, 2012

### maCrobo

Yes it always true, either if f(x) is continuos on [a,b] or on (a,b). In the first case you have a proper integral, in fact the primitive F(x) is also continuos and the limit is the value of F at a (or b). In the second case you have an improper integral and in that case is necessary to use the limit to check whether or not the result is a finite value.

5. Jan 14, 2012

### GreenPrint

hmmm...
ya i guess so thanks