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

Integral of 3+2x-x^2 dx

The solution

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

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

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

Detail solution

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

$\frac{x \left(- x^{2} + 3 x + 9\right)}{3}$
Add the constant of integration:

$\frac{x \left(- x^{2} + 3 x + 9\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x^{2} + 3 x + 9\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$9$$

Numerical answer [src]

9.0

9.0

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

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Integral of 3+2x-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution