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Solving integrals/ cos(2*x-1)

Integral of cos(2*x-1) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                
 --                
 2                 
  /                
 |                 
 |  cos(2*x - 1) dx
 |                 
/                  
pi                 
--                 
3
$$\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \cos{\left(2 x - 1 \right)}\, dx$$ 
Integral(cos(2*x - 1), (x, pi/3, pi/2))
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 cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                  
 |                       sin(2*x - 1)
 | cos(2*x - 1) dx = C + ------------
 |                            2      
/
$$\int \cos{\left(2 x - 1 \right)}\, dx = C + \frac{\sin{\left(2 x - 1 \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
            /    pi\
         sin|1 + --|
sin(1)      \    3 /
------ - -----------
  2           2
$$- \frac{\sin{\left(1 + \frac{\pi}{3} \right)}}{2} + \frac{\sin{\left(1 \right)}}{2}$$ 
=
= 
            /    pi\
         sin|1 + --|
sin(1)      \    3 /
------ - -----------
  2           2
$$- \frac{\sin{\left(1 + \frac{\pi}{3} \right)}}{2} + \frac{\sin{\left(1 \right)}}{2}$$ 
sin(1)/2 - sin(1 + pi/3)/2
Numerical answer [src] 
-0.0235900151005854
-0.0235900151005854

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

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