Mister Exam

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Integral of d{x}:
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Integral of x^3/(x-1)
Graphing y =:
x^3-8
Factor polynomial:
x^3-8
Plot:
x^3-8
Identical expressions
x^ three - eight
x cubed minus 8
x to the power of three minus eight
x3-8
x³-8
x to the power of 3-8
x^3-8dx
Similar expressions
x^3+8

Integral of x^3-8 dx

The solution

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  2            
  /            
 |             
 |  / 3    \   
 |  \x  - 8/ dx
 |             
/              
-1

$$\int\limits_{-1}^{2} \left(x^{3} - 8\right)\, dx$$

Integral(x^3 - 8, (x, -1, 2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-8\right)\, dx = - 8 x$
The result is: $\frac{x^{4}}{4} - 8 x$
Now simplify:

$\frac{x \left(x^{3} - 32\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} - 32\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 32\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                          4
 | / 3    \                x 
 | \x  - 8/ dx = C - 8*x + --
 |                         4 
/

$$\int \left(x^{3} - 8\right)\, dx = C + \frac{x^{4}}{4} - 8 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-81/4

$$- \frac{81}{4}$$

-81/4

$$- \frac{81}{4}$$

-81/4

Numerical answer [src]

-20.25

-20.25

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

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Identical expressions

Similar expressions

Integral of x^3-8 dx

Limits of integration:

The graph:

Piecewise:

The solution