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e^(-4x)
Solving integrals/ e^(-4x)

Integral of e^(-4x) dx

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The graph:

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The solution

You have entered [src] 
  1         
  /         
 |          
 |   -4*x   
 |  E     dx
 |          
/           
0
∫01e−4x dx\int\limits_{0}^{1} e^{- 4 x}\, dx 
Integral(E^(-4*x), (x, 0, 1))
Detail solution

  1. Let u=−4xu = - 4 x.

    Then let du=−4dxdu = - 4 dx and substitute −du4- \frac{du}{4}:

    ∫(−eu4) du\int \left(- \frac{e^{u}}{4}\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: −eu4- \frac{e^{u}}{4}

    Now substitute uu back in:

    −e−4x4- \frac{e^{- 4 x}}{4}

  2. Add the constant of integration:

    −e−4x4+constant- \frac{e^{- 4 x}}{4}+ \mathrm{constant}

The answer is:

−e−4x4+constant- \frac{e^{- 4 x}}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    
 |                 -4*x
 |  -4*x          e    
 | E     dx = C - -----
 |                  4  
/
∫e−4x dx=C−e−4x4\int e^{- 4 x}\, dx = C - \frac{e^{- 4 x}}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-1
Plot the graph f(x)
The answer [src] 
     -4
1   e  
- - ---
4    4
14−14e4\frac{1}{4} - \frac{1}{4 e^{4}} 
=
= 
     -4
1   e  
- - ---
4    4
14−14e4\frac{1}{4} - \frac{1}{4 e^{4}} 
1/4 - exp(-4)/4
Numerical answer [src] 
0.245421090277816
0.245421090277816
The graph
Integral of e^(-4x) dx

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

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