Solving a Confusing Integral: ∫0∞e-t dt

[_Steve_]

Homework Statement

∫₀^∞e^-t dt
(integral from 0 -> ∞)

Homework Equations

The Attempt at a Solution

so far, i have...
∫₀^∞e^-t dt
={-e^-t}₀^∞
= -e^-∞ - -e⁰
= 0 + 1 = 1

but looking at a graph, it approaches zero. What am I doing wrong??

 

[tiny-tim]

Welcome to PF!

Hi _Steve_! Welcome to PF!

but looking at a graph, it approaches zero. What am I doing wrong??

Nothing!

The graph starts at 1, and ends approaching zero.

The integral is the area under it, and it's so thin at the "infinity" end that the total area is 1.

 

[_Steve_]

Oh, hahaha, now I feel like an idiot
Thanks!

 

[tiny-tim]

Oh, hahaha, now I feel like an idiot
Thanks!

he he!

my work here is done! ​