Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/(x^2-2*x)
Integral of x/(sinx^2)^2
Integral of -x^2+9
Integral of (x+1)(x^2-2)
Graphing y =:
-x^2-x+2
Factor squared:
-x^2-x+2
Factor polynomial:
-x^2-x+2
Identical expressions
-x^ two -x+ two
minus x squared minus x plus 2
minus x to the power of two minus x plus two
-x2-x+2
-x²-x+2
-x to the power of 2-x+2
-x^2-x+2dx
Similar expressions
-x^2+x+2
x^2-x+2
-x^2-x-2

Solving integrals/ -x^2-x+2

Integral of -x^2-x+2 dx

The solution

You have entered [src]

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

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

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

$\frac{x \left(- 2 x^{2} - 3 x + 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(- 2 x^{2} - 3 x + 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- 2 x^{2} - 3 x + 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/2

$$\frac{9}{2}$$

9/2

$$\frac{9}{2}$$

9/2

Numerical answer [src]

4.5

4.5

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of -x^2-x+2 dx

Limits of integration:

The graph:

Piecewise:

The solution