Integral of 7x-14 dx

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 |  (7*x - 14) dx
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\int\limits_{2}^{5} \left(7 x - 14\right)\, dx

Integral(7*x - 14, (x, 2, 5))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 7 x\, dx = 7 \int x\, dx$
  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: $\frac{7 x^{2}}{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-14\right)\, dx = - 14 x$
The result is: $\frac{7 x^{2}}{2} - 14 x$
Now simplify:

$\frac{7 x \left(x - 4\right)}{2}$
Add the constant of integration:

$\frac{7 x \left(x - 4\right)}{2}+ \mathrm{constant}$

The answer is:

\frac{7 x \left(x - 4\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src]

  /                              2
 |                            7*x 
 | (7*x - 14) dx = C - 14*x + ----
 |                             2  
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\int \left(7 x - 14\right)\, dx = C + \frac{7 x^{2}}{2} - 14 x

Simplify

The graph

Plot the graph f(x)

The answer [src]

63/2

\frac{63}{2}

63/2

\frac{63}{2}

63/2

Numerical answer [src]

31.5

31.5

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