Integral of 2x-1/3 dx

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  2               
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 |  (2*x - 1/3) dx
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1

$$\int\limits_{1}^{2} \left(2 x - \frac{1}{3}\right)\, dx$$

Integral(2*x - 1/3, (x, 1, 2))

Detail solution

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

$x \left(x - \frac{1}{3}\right)$
Add the constant of integration:

$x \left(x - \frac{1}{3}\right)+ \mathrm{constant}$

The answer is:

$x \left(x - \frac{1}{3}\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                           
 |                       2   x
 | (2*x - 1/3) dx = C + x  - -
 |                           3
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$$\int \left(2 x - \frac{1}{3}\right)\, dx = C + x^{2} - \frac{x}{3}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

8/3

$$\frac{8}{3}$$

8/3

$$\frac{8}{3}$$

8/3

Numerical answer [src]

2.66666666666667

2.66666666666667

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