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Integral of -x^2+9x-18
Identical expressions
-x^ two +9x- eighteen
minus x squared plus 9x minus 18
minus x to the power of two plus 9x minus eighteen
-x2+9x-18
-x²+9x-18
-x to the power of 2+9x-18
-x^2+9x-18dx
Similar expressions
-x^2+9x+18
x^2+9x-18
-x^2-9x-18

Solving integrals/ -x^2+9x-18

Integral of -x^2+9x-18 dx

The solution

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  6                     
  /                     
 |                      
 |  /   2           \   
 |  \- x  + 9*x - 18/ dx
 |                      
/                       
3

$$\int\limits_{3}^{6} \left(\left(- x^{2} + 9 x\right) - 18\right)\, dx$$

Integral(-x^2 + 9*x - 18, (x, 3, 6))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- x^{2}\right)\, dx = - \int x^{2}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{2}\, dx = \frac{x^{3}}{3}$
    So, the result is: $- \frac{x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 9 x\, dx = 9 \int x\, dx$
    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: $\frac{9 x^{2}}{2}$
  The result is: $- \frac{x^{3}}{3} + \frac{9 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-18\right)\, dx = - 18 x$
The result is: $- \frac{x^{3}}{3} + \frac{9 x^{2}}{2} - 18 x$
Now simplify:

$\frac{x \left(- 2 x^{2} + 27 x - 108\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} + 27 x - 108\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} + 27 x - 108\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                                    3      2
 | /   2           \                 x    9*x 
 | \- x  + 9*x - 18/ dx = C - 18*x - -- + ----
 |                                   3     2  
/

$$\int \left(\left(- x^{2} + 9 x\right) - 18\right)\, dx = C - \frac{x^{3}}{3} + \frac{9 x^{2}}{2} - 18 x$$

Simplify

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Plot the graph f(x)

The answer [src]

9/2

$$\frac{9}{2}$$

9/2

$$\frac{9}{2}$$

9/2

Numerical answer [src]

4.5

4.5

The graph

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

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Integral of -x^2+9x-18 dx

Limits of integration:

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Piecewise:

The solution