Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 4x
Integral of 1/(x^3)
Integral of sinxdx
Integral of 4dx
Identical expressions
e^(x- twenty)
e to the power of (x minus 20)
e to the power of (x minus twenty)
e(x-20)
ex-20
e^x-20
e^(x-20)dx
Similar expressions
e^(x+20)

Solving integrals/ e^(x-20)

Integral of e^(x-20) dx

The solution

You have entered [src]

  1           
  /           
 |            
 |   x - 20   
 |  E       dx
 |            
/             
0

$$\int\limits_{0}^{1} e^{x - 20}\, dx$$

Integral(E^(x - 20), (x, 0, 1))

Detail solution

There are multiple ways to do this integral.
Method #1
1. Let $u = x - 20$ .
  
  Then let $du = dx$ and substitute $du$ :
  
  $\int e^{u}\, du$
  1. The integral of the exponential function is itself.
    
    $\int e^{u}\, du = e^{u}$
  Now substitute $u$ back in:
  
  $e^{x - 20}$
Method #2
1. Rewrite the integrand:
  
  $e^{x - 20} = \frac{e^{x}}{e^{20}}$
2. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{e^{x}}{e^{20}}\, dx = \frac{\int e^{x}\, dx}{e^{20}}$
  1. The integral of the exponential function is itself.
    
    $\int e^{x}\, dx = e^{x}$
  So, the result is: $\frac{e^{x}}{e^{20}}$
Now simplify:

$e^{x - 20}$
Add the constant of integration:

$e^{x - 20}+ \mathrm{constant}$

The answer is:

$e^{x - 20}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 |  x - 20           x - 20
 | E       dx = C + e      
 |                         
/

$$\int e^{x - 20}\, dx = C + e^{x - 20}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   -20    -19
- e    + e

$$- \frac{1}{e^{20}} + e^{-19}$$

=

   -20    -19
- e    + e

$$- \frac{1}{e^{20}} + e^{-19}$$

-exp(-20) + exp(-19)

Numerical answer [src]

3.54164281509871e-9

3.54164281509871e-9

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