Mister Exam

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Graphing y =:
x^2-2*x+4
Factor squared:
x^2-2*x+4
Identical expressions
x^ two - two *x+ four
x squared minus 2 multiply by x plus 4
x to the power of two minus two multiply by x plus four
x2-2*x+4
x²-2*x+4
x to the power of 2-2*x+4
x^2-2x+4
x2-2x+4
x^2-2*x+4dx
Similar expressions
x^2+2*x+4
x^2-2*x-4

Integral of x^2-2*x+4 dx

The solution

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  1                  
  /                  
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 |  / 2          \   
 |  \x  - 2*x + 4/ dx
 |                   
/                    
-2

$$\int\limits_{-2}^{1} \left(\left(x^{2} - 2 x\right) + 4\right)\, dx$$

Integral(x^2 - 2*x + 4, (x, -2, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 2 x\right)\, dx = - 2 \int x\, dx$
    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: $- x^{2}$
  The result is: $\frac{x^{3}}{3} - x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
The result is: $\frac{x^{3}}{3} - x^{2} + 4 x$
Now simplify:

$\frac{x \left(x^{2} - 3 x + 12\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 3 x + 12\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 3 x + 12\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                     
 |                                     3
 | / 2          \           2         x 
 | \x  - 2*x + 4/ dx = C - x  + 4*x + --
 |                                    3 
/

$$\int \left(\left(x^{2} - 2 x\right) + 4\right)\, dx = C + \frac{x^{3}}{3} - x^{2} + 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$18$$

Numerical answer [src]

18.0

18.0

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

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Integral of x^2-2*x+4 dx

Limits of integration:

The graph:

Piecewise:

The solution