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Canonical form:
-2x^2+12x-10
Identical expressions
- two x^2+12x- ten
minus 2x squared plus 12x minus 10
minus two x squared plus 12x minus ten
-2x2+12x-10
-2x²+12x-10
-2x to the power of 2+12x-10
-2x^2+12x-10dx
Similar expressions
-2x^2+12x+10
-2x^2-12x-10
2x^2+12x-10

Integral of -2x^2+12x-10 dx

The solution

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  5                        
  /                        
 |                         
 |  /     2            \   
 |  \- 2*x  + 12*x - 10/ dx
 |                         
/                          
1

$$\int\limits_{1}^{5} \left(\left(- 2 x^{2} + 12 x\right) - 10\right)\, dx$$

Integral(-2*x^2 + 12*x - 10, (x, 1, 5))

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:
    
    $\int \left(- 2 x^{2}\right)\, dx = - 2 \int x^{2}\, dx$
    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: $- \frac{2 x^{3}}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 12 x\, dx = 12 \int x\, dx$
    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: $6 x^{2}$
  The result is: $- \frac{2 x^{3}}{3} + 6 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-10\right)\, dx = - 10 x$
The result is: $- \frac{2 x^{3}}{3} + 6 x^{2} - 10 x$
Now simplify:

$\frac{2 x \left(- x^{2} + 9 x - 15\right)}{3}$
Add the constant of integration:

$\frac{2 x \left(- x^{2} + 9 x - 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{2 x \left(- x^{2} + 9 x - 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                
 |                                                3
 | /     2            \                    2   2*x 
 | \- 2*x  + 12*x - 10/ dx = C - 10*x + 6*x  - ----
 |                                              3  
/

$$\int \left(\left(- 2 x^{2} + 12 x\right) - 10\right)\, dx = C - \frac{2 x^{3}}{3} + 6 x^{2} - 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

64/3

$$\frac{64}{3}$$

64/3

$$\frac{64}{3}$$

64/3

Numerical answer [src]

21.3333333333333

21.3333333333333

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

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Integral of -2x^2+12x-10 dx

Limits of integration:

The graph:

Piecewise:

The solution