Mister Exam

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Graphing y =:
x-3x^2
Derivative of:
x-3x^2
Identical expressions
x-3x^ two
x minus 3x squared
x minus 3x to the power of two
x-3x2
x-3x²
x-3x to the power of 2
x-3x^2dx
Similar expressions
x+3x^2
(4/x^2)+2*x-3*x^2

Integral of x-3x^2 dx

The solution

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

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

Integral(x - 3*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:
  
  $\int \left(- 3 x^{2}\right)\, dx = - 3 \int x^{2}\, dx$
  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: $- x^{3}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $- x^{3} + \frac{x^{2}}{2}$
Now simplify:

$x^{2} \left(\frac{1}{2} - x\right)$
Add the constant of integration:

$x^{2} \left(\frac{1}{2} - x\right)+ \mathrm{constant}$

The answer is:

$x^{2} \left(\frac{1}{2} - x\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2

$$- \frac{1}{2}$$

-1/2

$$- \frac{1}{2}$$

-1/2

Numerical answer [src]

-0.5

-0.5

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

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Identical expressions

Similar expressions

Integral of x-3x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution