Integral of 3x-12 dx

You have entered [src]

  4              
  /              
 |               
 |  (3*x - 12) dx
 |               
/                
5

$$\int\limits_{5}^{4} \left(3 x - 12\right)\, dx$$

Integral(3*x - 12, (x, 5, 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:
  
  $\int 3 x\, dx = 3 \int x\, dx$
  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: $\frac{3 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-12\right)\, dx = - 12 x$
The result is: $\frac{3 x^{2}}{2} - 12 x$
Now simplify:

$\frac{3 x \left(x - 8\right)}{2}$
Add the constant of integration:

$\frac{3 x \left(x - 8\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 x \left(x - 8\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-3/2

$$- \frac{3}{2}$$

-3/2

$$- \frac{3}{2}$$

-3/2

Numerical answer [src]

-1.5

-1.5

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