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

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

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  / 3      2    \   
 |  \x  - 3*x  + 2/ dx
 |                    
/                     
-2

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

Integral(x^3 - 3*x^2 + 2, (x, -2, 1))

Detail solution

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

$x \left(\frac{x^{3}}{4} - x^{2} + 2\right)$
Add the constant of integration:

$x \left(\frac{x^{3}}{4} - x^{2} + 2\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{3}}{4} - x^{2} + 2\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-27/4

$$- \frac{27}{4}$$

-27/4

$$- \frac{27}{4}$$

-27/4

Numerical answer [src]

-6.75

-6.75

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

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Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution