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Solving integrals/ exp(-x/2)

Integral of exp(-x/2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  3        
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0
∫03e(−1)x2 dx\int\limits_{0}^{3} e^{\frac{\left(-1\right) x}{2}}\, dx 
Integral(exp((-x)/2), (x, 0, 3))
Detail solution

  1. Let u=(−1)x2u = \frac{\left(-1\right) x}{2}.

    Then let du=−dx2du = - \frac{dx}{2} and substitute −2du- 2 du:

    ∫(−2eu) du\int \left(- 2 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: −2eu- 2 e^{u}

    Now substitute uu back in:

    −2e(−1)x2- 2 e^{\frac{\left(-1\right) x}{2}}

  2. Now simplify:

    −2e−x2- 2 e^{- \frac{x}{2}}

  3. Add the constant of integration:

    −2e−x2+constant- 2 e^{- \frac{x}{2}}+ \mathrm{constant}

The answer is:

−2e−x2+constant- 2 e^{- \frac{x}{2}}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    
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 |  -x              -x 
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 |   2               2 
 | e    dx = C - 2*e   
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∫e(−1)x2 dx=C−2e(−1)x2\int e^{\frac{\left(-1\right) x}{2}}\, dx = C - 2 e^{\frac{\left(-1\right) x}{2}}
Simplify
The graph
0.003.000.250.500.751.001.251.501.752.002.252.502.755-5
Plot the graph f(x)
The answer [src] 
       -3/2
2 - 2*e
2−2e322 - \frac{2}{e^{\frac{3}{2}}} 
=
= 
       -3/2
2 - 2*e
2−2e322 - \frac{2}{e^{\frac{3}{2}}} 
2 - 2*exp(-3/2)
Numerical answer [src] 
1.55373967970314
1.55373967970314

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

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