Mister Exam

# Integral of e^(x-y) dx

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### The solution

You have entered [src]
  1
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|   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:

  /
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|  x - y           x - y
| E      dx = C + e
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/                        
$$\int e^{x - y}\, dx = C + e^{x - y}$$
   -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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