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Integral of 2*cos(3*x) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  x              
  -              
  2              
  /              
 |               
 |  2*cos(3*x) dx
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0                
$$\int\limits_{0}^{\frac{x}{2}} 2 \cos{\left(3 x \right)}\, dx$$
Integral(2*cos(3*x), (x, 0, x/2))
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 cosine is sine:

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

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