1. ## improper integrals

$\displaystyle \int e^{2x}dx$ [-infinity,0]

I set this equal to the limit as x goes to -infinity and subbed in a for -infinity. Then I solved the definite improper integral getting= $\displaystyle \frac{e^{2x}}{2}$ . I got (1/2)-0 = 1/2. Did I do this right??

2. Originally Posted by saiyanmx89
$\displaystyle \int e^{2x}dx$ [-infinity,0]

I set this equal to the limit as x goes to -infinity and subbed in a for -infinity. Then I solved the definite improper integral getting= $\displaystyle \frac{e^{2x}}{2}$ . I got (1/2)-0 = 1/2. Did I do this right??
Correct.

3. Originally Posted by saiyanmx89
$\displaystyle \int e^{2x}dx$ [-infinity,0]

I set this equal to the limit as x goes to -infinity and subbed in a for -infinity. Then I solved the definite improper integral getting= $\displaystyle \frac{e^{2x}}{2}$ . I got (1/2)-0 = 1/2. Did I do this right??
$\displaystyle \lim_{a \to -\infty} \int_a^0 e^{2x} \, dx$

$\displaystyle \lim_{a \to -\infty} \left[\frac{1}{2}e^{2x}\right]_a^0$

$\displaystyle \lim_{a \to -\infty} \left[\frac{1}{2} - \frac{1}{2}e^{2a}\right] = \frac{1}{2}$