Integral of Cos(4x-2) dx

The solution

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  1                
  /                
 |                 
 |  cos(4*x - 2) dx
 |                 
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0

$$\int\limits_{0}^{1} \cos{\left(4 x - 2 \right)}\, dx$$

Integral(cos(4*x - 2), (x, 0, 1))

Detail solution

Let $u = 4 x - 2$ .

Then let $du = 4 dx$ and substitute $\frac{du}{4}$ :

$\int \frac{\cos{\left(u \right)}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{4}$
  1. The integral of cosine is sine:
    
    $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
  So, the result is: $\frac{\sin{\left(u \right)}}{4}$
Now substitute $u$ back in:

$\frac{\sin{\left(4 x - 2 \right)}}{4}$
Now simplify:

$\frac{\sin{\left(4 x - 2 \right)}}{4}$
Add the constant of integration:

$\frac{\sin{\left(4 x - 2 \right)}}{4}+ \mathrm{constant}$

The answer is:

$\frac{\sin{\left(4 x - 2 \right)}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       sin(4*x - 2)
 | cos(4*x - 2) dx = C + ------------
 |                            4      
/

$$\int \cos{\left(4 x - 2 \right)}\, dx = C + \frac{\sin{\left(4 x - 2 \right)}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(2)
------
  2

$$\frac{\sin{\left(2 \right)}}{2}$$

sin(2)
------
  2

$$\frac{\sin{\left(2 \right)}}{2}$$

sin(2)/2

Numerical answer [src]

0.454648713412841

0.454648713412841

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

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Integral of Cos(4x-2) dx

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The solution