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Integral of 3cosx/3-x dx

The solution

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  1                  
  /                  
 |                   
 |  /3*cos(x)    \   
 |  |-------- - x| dx
 |  \   3        /   
 |                   
/                    
0

$$\int\limits_{0}^{1} \left(- x + \frac{3 \cos{\left(x \right)}}{3}\right)\, dx$$

Integral((3*cos(x))/3 - x, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- x\right)\, dx = - \int x\, dx$
  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: $- \frac{x^{2}}{2}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{3 \cos{\left(x \right)}}{3}\, dx = \frac{\int 3 \cos{\left(x \right)}\, dx}{3}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 3 \cos{\left(x \right)}\, dx = 3 \int \cos{\left(x \right)}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $\sin{\left(x \right)}$
    So, the result is: $3 \sin{\left(x \right)}$
  So, the result is: $\sin{\left(x \right)}$
The result is: $- \frac{x^{2}}{2} + \sin{\left(x \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                   
 |                          2         
 | /3*cos(x)    \          x          
 | |-------- - x| dx = C - -- + sin(x)
 | \   3        /          2          
 |                                    
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/2 + sin(1)

$$- \frac{1}{2} + \sin{\left(1 \right)}$$

-1/2 + sin(1)

$$- \frac{1}{2} + \sin{\left(1 \right)}$$

-1/2 + sin(1)

Numerical answer [src]

0.341470984807897

0.341470984807897

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

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Integral of 3cosx/3-x dx

Limits of integration:

The graph:

Piecewise:

The solution