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Solving integrals/ e^-x

Integral of e^-x dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1       
  /       
 |        
 |   -x   
 |  E   dx
 |        
/         
0
∫01e−x dx\int\limits_{0}^{1} e^{- x}\, dx 
Integral(E^(-x), (x, 0, 1))
Detail solution

  1. Let u=−xu = - x.

    Then let du=−dxdu = - dx and substitute −du- du:

    ∫(−eu) 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:

      False\text{False}

      1. The integral of the exponential function is itself.

        ∫eu du=eu\int e^{u}\, du = e^{u}

      So, the result is: −eu- e^{u}

    Now substitute uu back in:

    −e−x- e^{- x}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                
 |                 
 |  -x           -x
 | E   dx = C - e  
 |                 
/
∫e−x dx=C−e−x\int e^{- x}\, dx = C - e^{- x}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
     -1
1 - e
1−e−11 - e^{-1} 
=
= 
     -1
1 - e
1−e−11 - e^{-1} 
1 - exp(-1)
Numerical answer [src] 
0.632120558828558
0.632120558828558
The graph
Integral of e^-x dx

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

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