Mister Exam

Integral of sin6x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |  sin(6*x) dx
 |             
/              
0              
$$\int\limits_{0}^{1} \sin{\left(6 x \right)}\, dx$$
Integral(sin(6*x), (x, 0, 1))
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(6*x)
 | sin(6*x) dx = C - --------
 |                      6    
/                            
$$-{{\cos \left(6\,x\right)}\over{6}}$$
The answer [src]
1   cos(6)
- - ------
6     6   
$${{1}\over{6}}-{{\cos 6}\over{6}}$$
=
=
1   cos(6)
- - ------
6     6   
$$\frac{1}{6} - \frac{\cos{\left(6 \right)}}{6}$$
Numerical answer [src]
0.00663828555827233
0.00663828555827233

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