Integral of cos(3x-pi) dx

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

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

Simplify

Detail solution

Let $u = 3 x - \pi$ .

Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :

$\int \frac{\cos{\left(u \right)}}{9}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\cos{\left(u \right)}}{3}\, du = \frac{\int \cos{\left(u \right)}\, du}{3}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{3}$
Now substitute $u$ back in:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                               
 |                        sin(3*x)
 | cos(3*x - pi) dx = C - --------
 |                           3    
/

$${{\sin \left(3\,x-\pi\right)}\over{3}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  sin(3)   sin(6)
- ------ - ------
    3        3

$${{\sin \left(\pi+3\right)}\over{3}}-{{\sin \left(\pi-6\right) }\over{3}}$$

  sin(3)   sin(6)
- ------ - ------
    3        3

$$- \frac{\sin{\left(3 \right)}}{3} - \frac{\sin{\left(6 \right)}}{3}$$

Simplify

Numerical answer [src]

0.0460984967130195

0.0460984967130195

The graph

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