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Integral of (-2/3)(sen(4x)dx) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1               
  /               
 |                
 |  -2*sin(4*x)   
 |  ----------- dx
 |       3        
 |                
/                 
0                 
$$\int\limits_{0}^{1} \left(- \frac{2 \sin{\left(4 x \right)}}{3}\right)\, dx$$
Integral(-2*sin(4*x)/3, (x, 0, 1))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Let .

      Then let and substitute :

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

        1. The integral of sine is negative cosine:

        So, the result is:

      Now substitute back in:

    So, the result is:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                             
 |                              
 | -2*sin(4*x)          cos(4*x)
 | ----------- dx = C + --------
 |      3                  6    
 |                              
/                               
$$\int \left(- \frac{2 \sin{\left(4 x \right)}}{3}\right)\, dx = C + \frac{\cos{\left(4 x \right)}}{6}$$
The graph
The answer [src]
  1   cos(4)
- - + ------
  6     6   
$$- \frac{1}{6} + \frac{\cos{\left(4 \right)}}{6}$$
=
=
  1   cos(4)
- - + ------
  6     6   
$$- \frac{1}{6} + \frac{\cos{\left(4 \right)}}{6}$$
-1/6 + cos(4)/6
Numerical answer [src]
-0.275607270143935
-0.275607270143935

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