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sin(x-pi/3)
Solving integrals/ sin(x-pi/3)

Integral of sin(x-pi/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     /    pi\   
 |  sin|x - --| dx
 |     \    3 /   
 |                
/                 
0
$$\int\limits_{0}^{1} \sin{\left(x - \frac{\pi}{3} \right)}\, dx$$ 
Integral(sin(x - pi/3), (x, 0, 1))
Detail solution

  1. Let .

    Then let and substitute :

    1. The integral of sine is negative cosine:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                                 
 |    /    pi\             /    pi\
 | sin|x - --| dx = C - cos|x - --|
 |    \    3 /             \    3 /
 |                                 
/
$$\int \sin{\left(x - \frac{\pi}{3} \right)}\, dx = C - \cos{\left(x - \frac{\pi}{3} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
1      /    pi\
- - sin|1 + --|
2      \    6 /
$$\frac{1}{2} - \sin{\left(\frac{\pi}{6} + 1 \right)}$$ 
=
= 
1      /    pi\
- - sin|1 + --|
2      \    6 /
$$\frac{1}{2} - \sin{\left(\frac{\pi}{6} + 1 \right)}$$ 
1/2 - sin(1 + pi/6)
Numerical answer [src] 
-0.498886402325218
-0.498886402325218
The graph
Integral of sin(x-pi/3) dx

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

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