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Integral of d{x}:
Integral of xe
Integral of sin(e^x)
Integral of 3x²
Integral of e^-t
Derivative of:
e^-t
Identical expressions
e^-t
e to the power of minus t
e-t
Similar expressions
e^+t

Solving integrals/ e^-t

Integral of e^-t dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} e^{- t}\, dt$$

Integral(E^(-t), (t, 0, 1))

Detail solution

Let $u = - t$ .

Then let $du = - dt$ and substitute $- du$ :

$\int \left(- e^{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $- e^{u}$
Now substitute $u$ back in:

$- e^{- t}$
Add the constant of integration:

$- e^{- t}+ \mathrm{constant}$

The answer is:

$- e^{- t}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                
 |                 
 |  -t           -t
 | E   dt = C - e  
 |                 
/

$$\int e^{- t}\, dt = C - e^{- t}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

     -1
1 - e

$$1 - e^{-1}$$

=

     -1
1 - e

$$1 - e^{-1}$$

1 - exp(-1)

Numerical answer [src]

0.632120558828558

0.632120558828558

The graph

Integral of e^-t dx

Use the examples entering the upper and lower limits of integration.