Integral of 3*sin(4x) dx

You have entered [src]

 pi              
 --              
 4               
  /              
 |               
 |  3*sin(4*x) dx
 |               
/                
0

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

Integral(3*sin(4*x), (x, 0, pi/4))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.5

1.5

The graph

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