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Integral of e^(x-y) dx

Limits of integration:

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Enter:

The solution

You have entered [src]
  1          
  /          
 |           
 |   x - y   
 |  E      dx
 |           
/            
0            
$$\int\limits_{0}^{1} e^{x - y}\, dx$$
Integral(E^(x - y), (x, 0, 1))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Let .

      Then let and substitute :

      1. The integral of the exponential function is itself.

      Now substitute back in:

    Method #2

    1. Rewrite the integrand:

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

      1. The integral of the exponential function is itself.

      So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                      
 |                       
 |  x - y           x - y
 | E      dx = C + e     
 |                       
/                        
$$\int e^{x - y}\, dx = C + e^{x - y}$$
The answer [src]
   -y    1 - y
- e   + e     
$$e^{1 - y} - e^{- y}$$
=
=
   -y    1 - y
- e   + e     
$$e^{1 - y} - e^{- y}$$
-exp(-y) + exp(1 - y)

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

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