Integral of sin(2x-1) dx

The solution

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 |  sin(2*x - 1) dx
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0

$$\int\limits_{0}^{1} \sin{\left(2 x - 1 \right)}\, dx$$

Integral(sin(2*x - 1*1), (x, 0, 1))

Detail solution

Let $u = 2 x - 1$ .

Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :

$\int \frac{\sin{\left(u \right)}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{\sin{\left(u \right)}}{2}\, du = \frac{\int \sin{\left(u \right)}\, du}{2}$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- \frac{\cos{\left(u \right)}}{2}$
Now substitute $u$ back in:

$- \frac{\cos{\left(2 x - 1 \right)}}{2}$
Now simplify:

$- \frac{\cos{\left(2 x - 1 \right)}}{2}$
Add the constant of integration:

$- \frac{\cos{\left(2 x - 1 \right)}}{2}+ \mathrm{constant}$

The answer is:

$- \frac{\cos{\left(2 x - 1 \right)}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                  
 |                       cos(2*x - 1)
 | sin(2*x - 1) dx = C - ------------
 |                            2      
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$$-{{\cos \left(2\,x-1\right)}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Simplify

Numerical answer [src]

1.28230080812608e-23

1.28230080812608e-23

The graph

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

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Integral of sin(2x-1) dx

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The solution