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sin(6x-2)

Solving integrals/ sin(6x+2)

Integral of sin(6x+2) dx

The solution

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  1                
  /                
 |                 
 |  sin(6*x + 2) dx
 |                 
/                  
0

$$\int\limits_{0}^{1} \sin{\left(6 x + 2 \right)}\, dx$$

Integral(sin(6*x + 2), (x, 0, 1))

Detail solution

Let $u = 6 x + 2$ .

Then let $du = 6 dx$ and substitute $\frac{du}{6}$ :

$\int \frac{\sin{\left(u \right)}}{36}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(u \right)}}{6}\, du = \frac{\int \sin{\left(u \right)}\, du}{6}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{6}$
Now substitute $u$ back in:

$- \frac{\cos{\left(6 x + 2 \right)}}{6}$
Now simplify:

$- \frac{\cos{\left(6 x + 2 \right)}}{6}$
Add the constant of integration:

$- \frac{\cos{\left(6 x + 2 \right)}}{6}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(6 x + 2 \right)}}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       cos(6*x + 2)
 | sin(6*x + 2) dx = C - ------------
 |                            6      
/

$$\int \sin{\left(6 x + 2 \right)}\, dx = C - \frac{\cos{\left(6 x + 2 \right)}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

  cos(8)   cos(2)
- ------ + ------
    6        6

$$\frac{\cos{\left(2 \right)}}{6} - \frac{\cos{\left(8 \right)}}{6}$$

  cos(8)   cos(2)
- ------ + ------
    6        6

$$\frac{\cos{\left(2 \right)}}{6} - \frac{\cos{\left(8 \right)}}{6}$$

Упростить

Numerical answer [src]

-0.0451078004564215

-0.0451078004564215

The graph

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

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Integral of sin(6x+2) dx

Limits of integration:

The graph:

Piecewise:

The solution