Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x*e^(4*x)
Integral of x/sqrt(x^2-4x+1)
Integral of x/(x^2-1)^3
Integral of x*dx
Graphing y =:
2x^2-4x
Identical expressions
two x^2-4x
2x squared minus 4x
two x squared minus 4x
2x2-4x
2x²-4x
2x to the power of 2-4x
2x^2-4xdx
Similar expressions
2x^2+4x
(x+8)/(-2*x^2-4*x+6)

Integral of 2x^2-4x dx

The solution

You have entered [src]

  0                
  /                
 |                 
 |  /   2      \   
 |  \2*x  - 4*x/ dx
 |                 
/                  
-3

$$\int\limits_{-3}^{0} \left(2 x^{2} - 4 x\right)\, dx$$

Integral(2*x^2 - 4*x, (x, -3, 0))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$36$$

Numerical answer [src]

36.0

36.0

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 2x^2-4x dx

Limits of integration:

The graph:

Piecewise:

The solution