Mister Exam

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Integral of d{x}:
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Integral of x^2/(1-x^4)
Derivative of:
8-x^2
Graphing y =:
8-x^2
8-x^2
Identical expressions
eight -x^ two
8 minus x squared
eight minus x to the power of two
8-x2
8-x²
8-x to the power of 2
8-x^2dx
Similar expressions
8+x^2

Integral of 8-x^2 dx

The solution

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  3            
  /            
 |             
 |  /     2\   
 |  \8 - x / dx
 |             
/              
2

$$\int\limits_{2}^{3} \left(8 - x^{2}\right)\, dx$$

Integral(8 - x^2, (x, 2, 3))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 8\, dx = 8 x$
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: $- \frac{x^{3}}{3} + 8 x$
Now simplify:

$\frac{x \left(24 - x^{2}\right)}{3}$
Add the constant of integration:

$\frac{x \left(24 - x^{2}\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(24 - x^{2}\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                          3
 | /     2\                x 
 | \8 - x / dx = C + 8*x - --
 |                         3 
/

$$\int \left(8 - x^{2}\right)\, dx = C - \frac{x^{3}}{3} + 8 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/3

$$\frac{5}{3}$$

5/3

$$\frac{5}{3}$$

5/3

Numerical answer [src]

1.66666666666667

1.66666666666667

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

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Integral of 8-x^2 dx

Limits of integration:

The graph:

Piecewise:

The solution