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Integral of 2/3sin(3x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
 pi              
 --              
 4               
  /              
 |               
 |  2*sin(3*x)   
 |  ---------- dx
 |      3        
 |               
/                
pi               
--               
6                
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{2 \sin{\left(3 x \right)}}{3}\, dx$$
Integral(2*sin(3*x)/3, (x, pi/6, pi/4))
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(3*x)          2*cos(3*x)
 | ---------- dx = C - ----------
 |     3                   9     
 |                               
/                                
$$\int \frac{2 \sin{\left(3 x \right)}}{3}\, dx = C - \frac{2 \cos{\left(3 x \right)}}{9}$$
The graph
The answer [src]
  ___
\/ 2 
-----
  9  
$$\frac{\sqrt{2}}{9}$$
=
=
  ___
\/ 2 
-----
  9  
$$\frac{\sqrt{2}}{9}$$
sqrt(2)/9
Numerical answer [src]
0.157134840263677
0.157134840263677

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