Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of ((1-x)/(1+x))^(1/2)
Integral of x*e^(5*x)*dx
Integral of (dx)/(sqrt(x^(2)+6x+10))
Integral of dx/((3*x^6))
Graphing y =:
3-2x-x^2
Canonical form:
3-2x-x^2
Identical expressions
three - two x-x^2
3 minus 2x minus x squared
three minus two x minus x squared
3-2x-x2
3-2x-x²
3-2x-x to the power of 2
3-2x-x^2dx
Similar expressions
3-2x+x^2
3+2x-x^2

Integral of 3-2x-x^2 dx

The solution

You have entered [src]

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

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

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

     ___
14*\/ 2 
--------
   3

$$\frac{14 \sqrt{2}}{3}$$

     ___
14*\/ 2 
--------
   3

$$\frac{14 \sqrt{2}}{3}$$

14*sqrt(2)/3

Numerical answer [src]

6.59966329107444

6.59966329107444

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 3-2x-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution