Mister Exam

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How to use it?
Integral of d{x}:
Integral of (x-1)^1/2
Integral of log(x)*dx/x^3
Integral of sin(log(x))^2/x
Integral of dx/(2*x-1)
Derivative of:
2e^(-x)
Identical expressions
2e^(-x)
2e to the power of ( minus x)
2e(-x)
2e-x
2e^-x
2e^(-x)dx
Similar expressions
(x+2)*e^(-x)
2e^(x)

Solving integrals/ 2e^(-x)

Integral of 2e^(-x) dx

The solution

You have entered [src]

  1         
  /         
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 |     -x   
 |  2*E   dx
 |          
/           
0

$$\int\limits_{0}^{1} 2 e^{- x}\, dx$$

Integral(2*E^(-x), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 2 e^{- x}\, dx = 2 \int e^{- x}\, dx$
1. 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:
  
  $- e^{- x}$
So, the result is: $- 2 e^{- x}$
Add the constant of integration:

$- 2 e^{- x}+ \mathrm{constant}$

The answer is:

$- 2 e^{- x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                    
 |                     
 |    -x             -x
 | 2*E   dx = C - 2*e  
 |                     
/

$$\int 2 e^{- x}\, dx = C - 2 e^{- x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       -1
2 - 2*e

$$2 - \frac{2}{e}$$

=

       -1
2 - 2*e

$$2 - \frac{2}{e}$$

2 - 2*exp(-1)

Numerical answer [src]

1.26424111765712

1.26424111765712

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