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Solving integrals/ e^(x-y)

Integral of e^(x-y) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |   x - y   
 |  e      dx
 |           
/            
0
∫01ex−y dx\int\limits_{0}^{1} e^{x - y}\, dx
Simplify
Detail solution

  1. Rewrite the integrand:

    ex−y=exe−ye^{x - y} = e^{x} e^{- y}

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

    ∫exe−y dx=e−y∫ex dx\int e^{x} e^{- y}\, dx = e^{- y} \int e^{x}\, dx

    1. The integral of the exponential function is itself.

      ∫ex dx=ex\int e^{x}\, dx = e^{x}

    So, the result is: exe−ye^{x} e^{- y}

  3. Now simplify:

    ex−ye^{x - y}

  4. Add the constant of integration:

    ex−y+constante^{x - y}+ \mathrm{constant}

The answer is:

ex−y+constante^{x - y}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                       
 |  x - y           x  -y
 | e      dx = C + e *e  
 |                       
/
ex−ye^{x-y}
Simplify
The answer [src] 
   -y    1 - y
- e   + e
e1−y−e−ye^{1-y}-e^ {- y } 
=
= 
   -y    1 - y
- e   + e
e−y+1−e−ye^{- y + 1} - e^{- y}
Simplify

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

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