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sin(3*x)

Integral of sin(3*x) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
 pi            
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 2             
  /            
 |             
 |  sin(3*x) dx
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/              
0              
$$\int\limits_{0}^{\frac{\pi}{2}} \sin{\left(3 x \right)}\, dx$$
Integral(sin(3*x), (x, 0, pi/2))
Detail solution
  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:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                          
 |                   cos(3*x)
 | sin(3*x) dx = C - --------
 |                      3    
/                            
$$\int \sin{\left(3 x \right)}\, dx = C - \frac{\cos{\left(3 x \right)}}{3}$$
The graph
Numerical answer [src]
0.333333333333333
0.333333333333333
The graph
Integral of sin(3*x) dx

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