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Solving integrals/ -e^-x

Integral of -e^-x dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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

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

    ∫(−e−x) dx=−∫e−x dx\int \left(- e^{- x}\right)\, dx = - \int e^{- x}\, dx

    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}

    So, the result is: e−xe^{- x}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                 
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 |   -x           -x
 | -E   dx = C + e  
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∫(−e−x) dx=C+e−x\int \left(- e^{- x}\right)\, 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−1-1 + e^{-1} 
=
= 
      -1
-1 + e
−1+e−1-1 + 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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