Mister Exam

Integral of sin3x/3 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  t            
  /            
 |             
 |  sin(3*x)   
 |  -------- dx
 |     3       
 |             
/              
0              
$$\int\limits_{0}^{t} \frac{\sin{\left(3 x \right)}}{3}\, dx$$
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 - --------
 |    3                 9    
 |                           
/                            
$$-{{\cos \left(3\,x\right)}\over{9}}$$
The answer [src]
1   cos(3*t)
- - --------
9      9    
$$- \frac{\cos{\left(3 t \right)}}{9} + \frac{1}{9}$$
=
=
1   cos(3*t)
- - --------
9      9    
$$- \frac{\cos{\left(3 t \right)}}{9} + \frac{1}{9}$$

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