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Graphing y =:
-x²+2x+3
Identical expressions
-x²+2x+ three
minus x² plus 2x plus 3
minus x² plus 2x plus three
-x²+2x+3dx
Similar expressions
-x²+2x-3
-x²-2x+3
x²+2x+3

Integral of -x²+2x+3 dx

The solution

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

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

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

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

32/3

$$\frac{32}{3}$$

32/3

$$\frac{32}{3}$$

32/3

Numerical answer [src]

10.6666666666667

10.6666666666667

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

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Integral of -x²+2x+3 dx

Limits of integration:

The graph:

Piecewise:

The solution