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Integral of -7x+4 dx

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 10              
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 |  (-7*x + 4) dx
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1

$$\int\limits_{1}^{10} \left(4 - 7 x\right)\, dx$$

Integral(-7*x + 4, (x, 1, 10))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 7 x\right)\, dx = - 7 \int x\, dx$
  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: $- \frac{7 x^{2}}{2}$
The result is: $- \frac{7 x^{2}}{2} + 4 x$
Now simplify:

$\frac{x \left(8 - 7 x\right)}{2}$
Add the constant of integration:

$\frac{x \left(8 - 7 x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(8 - 7 x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             2
 |                           7*x 
 | (-7*x + 4) dx = C + 4*x - ----
 |                            2  
/

$$\int \left(4 - 7 x\right)\, dx = C - \frac{7 x^{2}}{2} + 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-621/2

$$- \frac{621}{2}$$

-621/2

$$- \frac{621}{2}$$

-621/2

Numerical answer [src]

-310.5

-310.5

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