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Integral of d{x}:
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Graphing y =:
x^2-4x+7
Canonical form:
x^2-4x+7
Identical expressions
x^ two -4x+ seven
x squared minus 4x plus 7
x to the power of two minus 4x plus seven
x2-4x+7
x²-4x+7
x to the power of 2-4x+7
x^2-4x+7dx
Similar expressions
x^2+4x+7
x^2-4x-7

Integral of x^2-4x+7 dx

The solution

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  2                  
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 |  / 2          \   
 |  \x  - 4*x + 7/ dx
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/                    
-1

$$\int\limits_{-1}^{2} \left(\left(x^{2} - 4 x\right) + 7\right)\, dx$$

Integral(x^2 - 4*x + 7, (x, -1, 2))

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:
    
    $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
    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: $- 2 x^{2}$
  The result is: $\frac{x^{3}}{3} - 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 7\, dx = 7 x$
The result is: $\frac{x^{3}}{3} - 2 x^{2} + 7 x$
Now simplify:

$\frac{x \left(x^{2} - 6 x + 21\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 6 x + 21\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 6 x + 21\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | / 2          \             2         x 
 | \x  - 4*x + 7/ dx = C - 2*x  + 7*x + --
 |                                      3 
/

$$\int \left(\left(x^{2} - 4 x\right) + 7\right)\, dx = C + \frac{x^{3}}{3} - 2 x^{2} + 7 x$$

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^2-4x+7 dx

Limits of integration:

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Piecewise:

The solution