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Integral of cos(x-pi/3) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

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

    Then let and substitute :

    1. The integral of cosine is sine:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                
 |                                 
 |    /    pi\             /    pi\
 | cos|x - --| dx = C + sin|x - --|
 |    \    3 /             \    3 /
 |                                 
/                                  
$$\int \cos{\left(x - \frac{\pi}{3} \right)}\, dx = C + \sin{\left(x - \frac{\pi}{3} \right)}$$
The graph
The answer [src]
  ___
\/ 3 
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  2  
$$\frac{\sqrt{3}}{2}$$
=
=
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\/ 3 
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  2  
$$\frac{\sqrt{3}}{2}$$
sqrt(3)/2
Numerical answer [src]
0.866025403784439
0.866025403784439

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