Mister Exam

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

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

The solution

You have entered [src]

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

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

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

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

$\frac{x \left(- x^{3} + 6 x - 8\right)}{4}$
Add the constant of integration:

$\frac{x \left(- x^{3} + 6 x - 8\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x^{3} + 6 x - 8\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-3/4

$$- \frac{3}{4}$$

-3/4

$$- \frac{3}{4}$$

-3/4

Numerical answer [src]

-0.75

-0.75

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

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

Limits of integration:

The graph:

Piecewise:

The solution