Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of x^2/(1+x^2)^2
Integral of e^(2x+3)
Integral of dx/(e^x+e^-x)
Integral of dx/sqrt(4x-x^2)
Graphing y =:
2-x^2
Factor polynomial:
2-x^2
Limit of the function:
2-x^2
Identical expressions
two -x^ two
2 minus x squared
two minus x to the power of two
2-x2
2-x²
2-x to the power of 2
2-x^2dx
Similar expressions
x/(sgrt(2-x^2))
2+x^2
x^3*(2-x)^2
x^4/((2-x^2)^(1/2))
dx/sqrt^3(2-x)^2
sqrt2-x^2

Integral of 2-x^2 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1/3

$$\frac{1}{3}$$

1/3

$$\frac{1}{3}$$

1/3

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 2-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution