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Integral of 4sin(3x) dx

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 |  4*sin(3*x) dx
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1

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

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

Detail solution

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

$\int 4 \sin{\left(3 x \right)}\, dx = 4 \int \sin{\left(3 x \right)}\, dx$
1. Let $u = 3 x$ .
  
  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:
  
  $- \frac{\cos{\left(3 x \right)}}{3}$
So, the result is: $- \frac{4 \cos{\left(3 x \right)}}{3}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                              
 |                     4*cos(3*x)
 | 4*sin(3*x) dx = C - ----------
 |                         3     
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

  4   4*cos(3)
- - + --------
  3      3

$$- \frac{4}{3} + \frac{4 \cos{\left(3 \right)}}{3}$$

  4   4*cos(3)
- - + --------
  3      3

$$- \frac{4}{3} + \frac{4 \cos{\left(3 \right)}}{3}$$

-4/3 + 4*cos(3)/3

Numerical answer [src]

-2.65332332880059

-2.65332332880059

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

Integral of 4*sin(3*x) dx