Integral of -x+3 dx

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  5            
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 |  (-x + 3) dx
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0

$$\int\limits_{0}^{5} \left(3 - x\right)\, dx$$

Integral(-x + 3, (x, 0, 5))

Detail solution

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

$\frac{x \left(6 - x\right)}{2}$
Add the constant of integration:

$\frac{x \left(6 - x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(6 - x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

5/2

$$\frac{5}{2}$$

5/2

$$\frac{5}{2}$$

5/2

Numerical answer [src]

2.5

2.5

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