Integral of e-x dx

You have entered [src]

  1           
  /           
 |            
 |  (E - x) dx
 |            
/             
0

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

Integral(E - x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int e\, dx = e x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- \frac{x^{2}}{2}$
The result is: $- \frac{x^{2}}{2} + e x$
Now simplify:

$\frac{x \left(- x + 2 e\right)}{2}$
Add the constant of integration:

$\frac{x \left(- x + 2 e\right)}{2}+ \mathrm{constant}$

The answer is:

\frac{x \left(- x + 2 e\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                  2      
 |                  x       
 | (E - x) dx = C - -- + E*x
 |                  2       
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2 + E

- \frac{1}{2} + e

-1/2 + E

- \frac{1}{2} + e

-1/2 + E

Numerical answer [src]

2.21828182845905

2.21828182845905

The graph

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