Question

evaluate the improper integral:
∫e^(-x) dx (from 0 to ∞)

Answer 1

1

Answer 2

please explain

Answer 3

i kept getting -1

Answer 4

\[\lim_{t\to\infty}\left.\int\limits_{0}^{t}e^{-x}dx=\lim_{t\to\infty}-e^{-x}\right|_{0}^{t}\]

\[=\lim_{t\to\infty}-e^{-t}+e^0=0+1=1\]

Answer 5

ok?

Answer 6

ok

Answer 7

wait why is -e^-t = 1?

Answer 8

-e^-t is not equal to 1

Answer 9

i know it's like -e/t...

Answer 10

u said 1 + 0 = 1

Answer 11

\[\lim_{t\to\infty}-e^{-t}=\lim_{t\to\infty}-\frac{1}{e^{t}}=0\]

Answer 12

thanks!