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Solving integrals/ sin(6x-П/3)

Integral of sin(6x-П/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     /      pi\   
 |  sin|6*x - --| dx
 |     \      3 /   
 |                  
/                   
0
$$\int\limits_{0}^{1} \sin{\left(6 x - \frac{\pi}{3} \right)}\, dx$$ 
Integral(sin(6*x - pi/3), (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. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                          /      pi\
 |                        cos|6*x - --|
 |    /      pi\             \      3 /
 | sin|6*x - --| dx = C - -------------
 |    \      3 /                6      
 |                                     
/
$$\int \sin{\left(6 x - \frac{\pi}{3} \right)}\, dx = C - \frac{\cos{\left(6 x - \frac{\pi}{3} \right)}}{6}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        /    pi\
     sin|6 + --|
1       \    6 /
-- - -----------
12        6
$$\frac{1}{12} - \frac{\sin{\left(\frac{\pi}{6} + 6 \right)}}{6}$$ 
=
= 
        /    pi\
     sin|6 + --|
1       \    6 /
-- - -----------
12        6
$$\frac{1}{12} - \frac{\sin{\left(\frac{\pi}{6} + 6 \right)}}{6}$$ 
1/12 - sin(6 + pi/6)/6
Numerical answer [src] 
0.043649296054362
0.043649296054362

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

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