Mister Exam

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Graphing y =:
2x^3-3x^2+1
Derivative of:
2x^3-3x^2+1
Identical expressions
two x^ three -3x^2+ one
2x cubed minus 3x squared plus 1
two x to the power of three minus 3x squared plus one
2x3-3x2+1
2x³-3x²+1
2x to the power of 3-3x to the power of 2+1
2x^3-3x^2+1dx
Similar expressions
2x^3+3x^2+1
2x^3-3x^2-1

Integral of 2x^3-3x^2+1 dx

The solution

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

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

Integral(2*x^3 - 3*x^2 + 1, (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:
    
    $\int 2 x^{3}\, dx = 2 \int x^{3}\, dx$
    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: $\frac{x^{4}}{2}$
  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: $\frac{x^{4}}{2} - x^{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{x^{4}}{2} - x^{3} + x$
Add the constant of integration:

$\frac{x^{4}}{2} - x^{3} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{4}}{2} - x^{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                      
 |                                 4     
 | /   3      2    \              x     3
 | \2*x  - 3*x  + 1/ dx = C + x + -- - x 
 |                                2      
/

$$\int \left(\left(2 x^{3} - 3 x^{2}\right) + 1\right)\, dx = C + \frac{x^{4}}{2} - x^{3} + x$$

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

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Integral of 2x^3-3x^2+1 dx

Limits of integration:

The graph:

Piecewise:

The solution