Mister Exam

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Integral of (2x+3)
Factor polynomial:
-x^2+3*x
Limit of the function:
-x^2+3*x
Identical expressions
-x^ two + three *x
minus x squared plus 3 multiply by x
minus x to the power of two plus three multiply by x
-x2+3*x
-x²+3*x
-x to the power of 2+3*x
-x^2+3x
-x2+3x
-x^2+3*xdx
Similar expressions
-x^2-3*x
x^2+3*x

Integral of -x^2+3*x dx

The solution

You have entered [src]

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

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

Integral(-x^2 + 3*x, (x, -2, 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. 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: $- \frac{x^{3}}{3} + \frac{3 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(9 - 2 x\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(9 - 2 x\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(9 - 2 x\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-16/3

$$- \frac{16}{3}$$

-16/3

$$- \frac{16}{3}$$

-16/3

Numerical answer [src]

-5.33333333333333

-5.33333333333333

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

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Identical expressions

Similar expressions

Integral of -x^2+3*x dx

Limits of integration:

The graph:

Piecewise:

The solution