Mister Exam

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Integral of dx/2-3x dx

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 |  (0.5 - 3*x) dx
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$$\int\limits_{0}^{1} \left(0.5 - 3 x\right)\, dx$$

Integral(0.5 - 3*x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 0.5\, dx = 0.5 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 3 x\right)\, dx = - 3 \int x\, dx$
  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: $- \frac{3 x^{2}}{2}$
The result is: $- \frac{3 x^{2}}{2} + 0.5 x$
Now simplify:

$\frac{x \left(1 - 3 x\right)}{2}$
Add the constant of integration:

$\frac{x \left(1 - 3 x\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(1 - 3 x\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        2        
 |                      3*x         
 | (0.5 - 3*x) dx = C - ---- + 0.5*x
 |                       2          
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$$\int \left(0.5 - 3 x\right)\, dx = C - \frac{3 x^{2}}{2} + 0.5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1.00000000000000

$$-1.0$$

-1.00000000000000

$$-1.0$$

-1.00000000000000

Numerical answer [src]

-1.0

-1.0

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