Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of e^(2*x+1)
Integral of e^x²
Integral of (-x)/(1+x^2)
Integral of sqrt(x^2+4)/x^2
Graphing y =:
-x^2-x
Plot:
-x^2-x
Identical expressions
-x^ two -x
minus x squared minus x
minus x to the power of two minus x
-x2-x
-x²-x
-x to the power of 2-x
-x^2-xdx
Similar expressions
x^2-x
-x^2+x

Solving integrals/ -x^2-x

Integral of -x^2-x dx

The solution

You have entered [src]

  1              
  /              
 |               
 |  /   2    \   
 |  \- x  - x/ dx
 |               
/                
0

$$\int\limits_{0}^{1} \left(- x^{2} - x\right)\, dx$$

Integral(-x^2 - x, (x, 0, 1))

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:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  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: $- \frac{x^{3}}{3} - \frac{x^{2}}{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-5/6

$$- \frac{5}{6}$$

-5/6

$$- \frac{5}{6}$$

-5/6

Numerical answer [src]

-0.833333333333333

-0.833333333333333

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 dx

Limits of integration:

The graph:

Piecewise:

The solution