Mister Exam

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Integral of d{x}:
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Integral of 4x^-2
Integral of x^3*e^(x*(-2))
Factor polynomial:
x+6-x^2
Identical expressions
x+ six -x^ two
x plus 6 minus x squared
x plus six minus x to the power of two
x+6-x2
x+6-x²
x+6-x to the power of 2
x+6-x^2dx
Similar expressions
x+6+x^2
x-6-x^2

Solving integrals/ x+6-x^2

Integral of x+6-x^2 dx

The solution

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  3                
  /                
 |                 
 |  /         2\   
 |  \x + 6 - x / dx
 |                 
/                  
-2

$$\int\limits_{-2}^{3} \left(- x^{2} + \left(x + 6\right)\right)\, dx$$

Integral(x + 6 - x^2, (x, -2, 3))

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 $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 6\, dx = 6 x$
  The result is: $\frac{x^{2}}{2} + 6 x$
The result is: $- \frac{x^{3}}{3} + \frac{x^{2}}{2} + 6 x$
Now simplify:

$\frac{x \left(- 2 x^{2} + 3 x + 36\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} + 3 x + 36\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} + 3 x + 36\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                   
 |                        2          3
 | /         2\          x          x 
 | \x + 6 - x / dx = C + -- + 6*x - --
 |                       2          3 
/

$$\int \left(- x^{2} + \left(x + 6\right)\right)\, dx = C - \frac{x^{3}}{3} + \frac{x^{2}}{2} + 6 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

125/6

$$\frac{125}{6}$$

125/6

$$\frac{125}{6}$$

125/6

Numerical answer [src]

20.8333333333333

20.8333333333333

The graph

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

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Identical expressions

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Integral of x+6-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution