Mister Exam

Lang:

Other calculators

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

Integral of 4x-2x^2 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                                 3
 | /         2\             2   2*x 
 | \4*x - 2*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]

$$0$$

Numerical answer [src]

1.26646615181459e-18

1.26646615181459e-18

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 4x-2x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution