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Identical expressions
twelve *sin(3x- four)
12 multiply by sinus of (3x minus 4)
twelve multiply by sinus of (3x minus four)
12sin(3x-4)
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12*sin(3x-4)dx
Similar expressions
12*sin(3x+4)

Integral of 12*sin(3x-4) dx

The solution

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 |  12*sin(3*x - 4) dx
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$$\int\limits_{0}^{1} 12 \sin{\left(3 x - 4 \right)}\, dx$$

Integral(12*sin(3*x - 4), (x, 0, 1))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int 12 \sin{\left(3 x - 4 \right)}\, dx = 12 \int \sin{\left(3 x - 4 \right)}\, dx$
1. Let $u = 3 x - 4$ .
  
  Then let $du = 3 dx$ and substitute $\frac{du}{3}$ :
  
  $\int \frac{\sin{\left(u \right)}}{3}\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \sin{\left(u \right)}\, du = \frac{\int \sin{\left(u \right)}\, du}{3}$
    1. The integral of sine is negative cosine:
      
      $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
    So, the result is: $- \frac{\cos{\left(u \right)}}{3}$
  Now substitute $u$ back in:
  
  $- \frac{\cos{\left(3 x - 4 \right)}}{3}$
So, the result is: $- 4 \cos{\left(3 x - 4 \right)}$
Now simplify:

$- 4 \cos{\left(3 x - 4 \right)}$
Add the constant of integration:

$- 4 \cos{\left(3 x - 4 \right)}+ \mathrm{constant}$

The answer is:

$- 4 \cos{\left(3 x - 4 \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | 12*sin(3*x - 4) dx = C - 4*cos(3*x - 4)
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$$\int 12 \sin{\left(3 x - 4 \right)}\, dx = C - 4 \cos{\left(3 x - 4 \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-4*cos(1) + 4*cos(4)

$$4 \cos{\left(4 \right)} - 4 \cos{\left(1 \right)}$$

-4*cos(1) + 4*cos(4)

$$4 \cos{\left(4 \right)} - 4 \cos{\left(1 \right)}$$

-4*cos(1) + 4*cos(4)

Numerical answer [src]

-4.77578370692701

-4.77578370692701

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

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Integral of 12*sin(3x-4) dx

Limits of integration:

The graph:

Piecewise:

The solution