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

In summary, the conversation discusses the integral from 0 to infinity of e^-t, which approaches zero at infinity. The solution provided is correct, and the graph confirms that the integral approaches zero.
  • #1
_Steve_
19
0

Homework Statement


0e-t dt
(integral from 0 -> ∞)

Homework Equations





The Attempt at a Solution


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

but looking at a graph, it approaches zero. What am I doing wrong??
 
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  • #2
Welcome to PF!

Hi _Steve_! Welcome to PF! :smile:
_Steve_ said:
but looking at a graph, it approaches zero. What am I doing wrong??

Nothing! :smile:

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. :wink:
 
  • #3
Oh, hahaha, now I feel like an idiot :tongue:
Thanks!
 
  • #4
_Steve_ said:
Oh, hahaha, now I feel like an idiot :tongue:
Thanks!

he he! :biggrin:

my work here is done! o:)
 

1. What is the purpose of solving this integral?

The purpose of solving this integral is to determine the area under the curve of the function y=e^-t from 0 to infinity. This can be useful in various applications such as calculating probabilities in statistics or solving differential equations in physics.

2. What is the general process for solving this type of integral?

The general process for solving this type of integral is to first identify any patterns or properties of the function, such as being continuous or having a finite limit at infinity. Then, evaluate the integral using techniques such as substitution, integration by parts, or partial fractions depending on the complexity of the function.

3. How do you handle the upper limit of infinity in this integral?

In this integral, the upper limit of infinity can be handled by taking the limit as the upper bound approaches infinity. This is done by evaluating the integral from 0 to a large number, and then taking the limit as that number approaches infinity. In this case, the limit will converge to a finite value.

4. Can this integral be solved using any other methods?

Yes, this integral can also be solved using techniques such as the Laplace transform or contour integration. However, these methods may require more advanced mathematical knowledge and may not be necessary for simpler integrals like this one.

5. What is the final solution for this integral?

The final solution for this integral is a definite value, which represents the area under the curve of the function y=e^-t from 0 to infinity. This value can be calculated using techniques such as numerical integration or by using a calculator or computer program.

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