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Graphing y =:
12-x^2
Identical expressions
twelve -x^ two
12 minus x squared
twelve minus x to the power of two
12-x2
12-x²
12-x to the power of 2
12-x^2dx
Similar expressions
12+x^2

Integral of 12-x^2 dx

The solution

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  1             
  /             
 |              
 |  /      2\   
 |  \12 - x / dx
 |              
/               
0

$$\int\limits_{0}^{1} \left(12 - x^{2}\right)\, dx$$

Integral(12 - x^2, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 12\, dx = 12 x$
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: $- \frac{x^{3}}{3} + 12 x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                            
 |                            3
 | /      2\                 x 
 | \12 - x / dx = C + 12*x - --
 |                           3 
/

$$\int \left(12 - x^{2}\right)\, dx = C - \frac{x^{3}}{3} + 12 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

35/3

$$\frac{35}{3}$$

35/3

$$\frac{35}{3}$$

35/3

Numerical answer [src]

11.6666666666667

11.6666666666667

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

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Integral of 12-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution