Mister Exam

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Integral of d{x}:
Integral of -1/y
Integral of e^(-x/2)
Integral of (x^2+1)e^-x
Integral of 4^(2*x)
Derivative of:
e^(-x/2)
Identical expressions
e^(-x/ two)
e to the power of ( minus x divide by 2)
e to the power of ( minus x divide by two)
e(-x/2)
e-x/2
e^-x/2
e^(-x divide by 2)
e^(-x/2)dx
Similar expressions
e^-x/2e^(-2x)
(e^x-e^-x)/2x
e^(x/2)

Solving integrals/ e^(-x/2)

Integral of e^(-x/2) dx

The solution

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$$\int\limits_{0}^{1} e^{\frac{\left(-1\right) x}{2}}\, dx$$

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

Detail solution

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

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

$\int \left(- 2 e^{u}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\text{False}$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  So, the result is: $- 2 e^{u}$
Now substitute $u$ back in:

$- 2 e^{\frac{\left(-1\right) x}{2}}$
Now simplify:

$- 2 e^{- \frac{x}{2}}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

$$\int e^{\frac{\left(-1\right) x}{2}}\, dx = C - 2 e^{\frac{\left(-1\right) x}{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

       -1/2
2 - 2*e

$$2 - \frac{2}{e^{\frac{1}{2}}}$$

       -1/2
2 - 2*e

$$2 - \frac{2}{e^{\frac{1}{2}}}$$

2 - 2*exp(-1/2)

Numerical answer [src]

0.786938680574733

0.786938680574733

The graph

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

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Identical expressions

Similar expressions

Integral of e^(-x/2) dx

Limits of integration:

The graph:

Piecewise:

The solution