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Solving integrals/ sin3x/2

Integral of sin3x/2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  sin(3*x)   
 |  -------- dx
 |     2       
 |             
/              
0
$$\int\limits_{0}^{1} \frac{\sin{\left(3 x \right)}}{2}\, dx$$ 
Integral(sin(3*x)/2, (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] 
  /                          
 |                           
 | sin(3*x)          cos(3*x)
 | -------- dx = C - --------
 |    2                 6    
 |                           
/
$$\int \frac{\sin{\left(3 x \right)}}{2}\, dx = C - \frac{\cos{\left(3 x \right)}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1   cos(3)
- - ------
6     6
$$\frac{1}{6} - \frac{\cos{\left(3 \right)}}{6}$$ 
=
= 
1   cos(3)
- - ------
6     6
$$\frac{1}{6} - \frac{\cos{\left(3 \right)}}{6}$$ 
1/6 - cos(3)/6
Numerical answer [src] 
0.331665416100074
0.331665416100074

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

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