Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 1/1+e^x
Integral of x^3/sqrt(1+x^2)
Integral of (-log(x))/x^2
Integral of dx/tan5x
Identical expressions
(3x- one)/ six
(3x minus 1) divide by 6
(3x minus one) divide by six
3x-1/6
(3x-1) divide by 6
(3x-1)/6dx
Similar expressions
(3x+1)/6

Solving integrals/ (3x-1)/6

Integral of (3x-1)/6 dx

The solution

You have entered [src]

  0           
  /           
 |            
 |  3*x - 1   
 |  ------- dx
 |     6      
 |            
/             
-5

$$\int\limits_{-5}^{0} \frac{3 x - 1}{6}\, dx$$

Integral((3*x - 1*1)/6, (x, -5, 0))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{3 x - 1}{6}\, dx = \frac{\int \left(3 x - 1\right)\, dx}{6}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 x\, dx = 3 \int x\, dx$
    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: $\frac{3 x^{2}}{2}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(\left(-1\right) 1\right)\, dx = - x$
  The result is: $\frac{3 x^{2}}{2} - x$
So, the result is: $\frac{x^{2}}{4} - \frac{x}{6}$
Now simplify:

$\frac{x \left(3 x - 2\right)}{12}$
Add the constant of integration:

$\frac{x \left(3 x - 2\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x - 2\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                       
 |                       2
 | 3*x - 1          x   x 
 | ------- dx = C - - + --
 |    6             6   4 
 |                        
/

$${{{{3\,x^2}\over{2}}-x}\over{6}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-85 
----
 12

$$-{{85}\over{12}}$$

-85 
----
 12

$$- \frac{85}{12}$$

Упростить

Numerical answer [src]

-7.08333333333333

-7.08333333333333

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (3x-1)/6 dx

Limits of integration:

The graph:

Piecewise:

The solution