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Solving integrals/ sin(2*x-pi/3)

Integral of sin(2*x-pi/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |     /      pi\   
 |  sin|2*x - --| dx
 |     \      3 /   
 |                  
/                   
0
$$\int\limits_{0}^{1} \sin{\left(2 x - \frac{\pi}{3} \right)}\, dx$$ 
Integral(sin(2*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|2*x - --|
 |    /      pi\             \      3 /
 | sin|2*x - --| dx = C - -------------
 |    \      3 /                2      
 |                                     
/
$$\int \sin{\left(2 x - \frac{\pi}{3} \right)}\, dx = C - \frac{\cos{\left(2 x - \frac{\pi}{3} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
       /    pi\
    sin|2 + --|
1      \    6 /
- - -----------
4        2
$$\frac{1}{4} - \frac{\sin{\left(\frac{\pi}{6} + 2 \right)}}{2}$$ 
=
= 
       /    pi\
    sin|2 + --|
1      \    6 /
- - -----------
4        2
$$\frac{1}{4} - \frac{\sin{\left(\frac{\pi}{6} + 2 \right)}}{2}$$ 
1/4 - sin(2 + pi/6)/2
Numerical answer [src] 
-0.0397006264766454
-0.0397006264766454

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

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