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Identical expressions
5x^ two - twenty
5x squared minus 20
5x to the power of two minus twenty
5x2-20
5x²-20
5x to the power of 2-20
5x^2-20dx
Similar expressions
5x^2+20

Integral of 5x^2-20 dx

The solution

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  1               
  /               
 |                
 |  /   2     \   
 |  \5*x  - 20/ dx
 |                
/                 
-2

$$\int\limits_{-2}^{1} \left(5 x^{2} - 20\right)\, dx$$

Integral(5*x^2 - 20, (x, -2, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 5 x^{2}\, dx = 5 \int x^{2}\, dx$
  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: $\frac{5 x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-20\right)\, dx = - 20 x$
The result is: $\frac{5 x^{3}}{3} - 20 x$
Now simplify:

$\frac{5 x \left(x^{2} - 12\right)}{3}$
Add the constant of integration:

$\frac{5 x \left(x^{2} - 12\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{5 x \left(x^{2} - 12\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                
 |                                3
 | /   2     \                 5*x 
 | \5*x  - 20/ dx = C - 20*x + ----
 |                              3  
/

$$\int \left(5 x^{2} - 20\right)\, dx = C + \frac{5 x^{3}}{3} - 20 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-45

$$-45$$

-45

$$-45$$

-45

Numerical answer [src]

-45.0

-45.0

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

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Integral of 5x^2-20 dx

Limits of integration:

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Piecewise:

The solution