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Integral of x^2-8x+16
Graphing y =:
x^2-8x+16
Identical expressions
x^ two -8x+ sixteen
x squared minus 8x plus 16
x to the power of two minus 8x plus sixteen
x2-8x+16
x²-8x+16
x to the power of 2-8x+16
x^2-8x+16dx
Similar expressions
x^2+8x+16
x^2-8x-16

Solving integrals/ x^2-8x+16

Integral of x^2-8x+16 dx

The solution

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  5                   
  /                   
 |                    
 |  / 2           \   
 |  \x  - 8*x + 16/ dx
 |                    
/                     
-1

$$\int\limits_{-1}^{5} \left(x^{2} - 8 x + 16\right)\, dx$$

Integral(x^2 - 8*x + 16, (x, -1, 5))

Detail solution

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:
  
  $\int \left(- 8 x\right)\, dx = - \int 8 x\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 8 x\, dx = 8 \int x\, dx$
    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: $4 x^{2}$
  So, the result is: $- 4 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 16\, dx = 16 x$
The result is: $\frac{x^{3}}{3} - 4 x^{2} + 16 x$
Now simplify:

$\frac{x \left(x^{2} - 12 x + 48\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 12 x + 48\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 12 x + 48\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | / 2           \             2          x 
 | \x  - 8*x + 16/ dx = C - 4*x  + 16*x + --
 |                                        3 
/

$${{x^3}\over{3}}-4\,x^2+16\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$42$$

Упростить

Numerical answer [src]

42.0

42.0

The graph

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

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Integral of x^2-8x+16 dx

Limits of integration:

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Piecewise:

The solution