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Graphing y =:
4x^3-2x^2
Identical expressions
4x^ three - two x^2
4x cubed minus 2x squared
4x to the power of three minus two x squared
4x3-2x2
4x³-2x²
4x to the power of 3-2x to the power of 2
4x^3-2x^2dx
Similar expressions
4x^3+2x^2

Solving integrals/ 4x^3-2x^2

Integral of 4x^3-2x^2 dx

The solution

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  1                 
  /                 
 |                  
 |  /   3      2\   
 |  \4*x  - 2*x / dx
 |                  
/                   
0

$$\int\limits_{0}^{1} \left(4 x^{3} - 2 x^{2}\right)\, dx$$

Integral(4*x^3 - 2*x^2, (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3

$${{1}\over{3}}$$

1/3

$$\frac{1}{3}$$

Simplify

Numerical answer [src]

0.333333333333333

0.333333333333333

The graph

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

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Integral of 4x^3-2x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution