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Solving integrals/ (2x-12x)

Integral of (2x-12x) dx

The solution

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 |  (2*x - 12*x) dx
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1

$$\int\limits_{1}^{4} \left(- 12 x + 2 x\right)\, dx$$

Integral(2*x - 12*x, (x, 1, 4))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 12 x\right)\, dx = - 12 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $- 6 x^{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $x^{2}$
The result is: $- 5 x^{2}$
Add the constant of integration:

$- 5 x^{2}+ \mathrm{constant}$

The answer is:

$- 5 x^{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | (2*x - 12*x) dx = C - 5*x 
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$$\int \left(- 12 x + 2 x\right)\, dx = C - 5 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-75

$$-75$$

=

-75

$$-75$$

-75

Numerical answer [src]

-75.0

-75.0

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