Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 5/x
Integral of x^1/3
Integral of ln^2(x)
Integral of exp(-x)
Limit of the function:
exp(-x)
Derivative of:
exp(-x)
Graphing y =:
exp(-x)
Identical expressions
exp(-x)
exponent of ( minus x)
exp-x
exp(-x)dx
Similar expressions
exp(x)
2x*exp(-x^2)
x^2*exp((-x^2)/2)

Solving integrals/ exp(-x)

Integral of exp(-x) dx

The solution

You have entered [src]

$$\int\limits_{0}^{1} e^{- x}\, dx$$

Integral(exp(-x), (x, 0, 1))

Detail solution

Let $u = - x$ .

Then let $du = - dx$ 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:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                
 |                 
 |  -x           -x
 | e   dx = C - e  
 |                 
/

$$\int e^{- x}\, dx = C - e^{- x}$$

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 exp(-x) dx

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