Mister Exam

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Limit of the function:
sin(4*x)/sin(2*x)
Identical expressions
sin(four *x)/sin(two *x)
sinus of (4 multiply by x) divide by sinus of (2 multiply by x)
sinus of (four multiply by x) divide by sinus of (two multiply by x)
sin(4x)/sin(2x)
sin4x/sin2x
sin(4*x) divide by sin(2*x)
sin(4*x)/sin(2*x)dx
Similar expressions
(1+sin4x)/(sin2x)^2

Solving integrals/ sin(4*x)/sin(2*x)

Integral of sin(4x)/sin(2x) dx

The solution

You have entered [src]

  1            
  /            
 |             
 |  sin(4*x)   
 |  -------- dx
 |  sin(2*x)   
 |             
/              
0

$$\int\limits_{0}^{1} \frac{\sin{\left(4 x \right)}}{\sin{\left(2 x \right)}}\, dx$$

Integral(sin(4*x)/sin(2*x), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\frac{\sin{\left(4 x \right)}}{\sin{\left(2 x \right)}} = 2 - 4 \sin^{2}{\left(x \right)}$
Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 2\, dx = 2 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- 4 \sin^{2}{\left(x \right)}\right)\, dx = - 4 \int \sin^{2}{\left(x \right)}\, dx$
  1. Rewrite the integrand:
    
    $\sin^{2}{\left(x \right)} = \frac{1}{2} - \frac{\cos{\left(2 x \right)}}{2}$
  2. Integrate term-by-term:
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int \frac{1}{2}\, dx = \frac{x}{2}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- \frac{\cos{\left(2 x \right)}}{2}\right)\, dx = - \frac{\int \cos{\left(2 x \right)}\, dx}{2}$
      1. Let $u = 2 x$ .
        
        Then let $du = 2 dx$ and substitute $\frac{du}{2}$ :
        
        $\int \frac{\cos{\left(u \right)}}{2}\, du$
        
        The integral of a constant times a function is the constant times the integral of the function:
        
        $\int \cos{\left(u \right)}\, du = \frac{\int \cos{\left(u \right)}\, du}{2}$
        
        The integral of cosine is sine:
        
        $\int \cos{\left(u \right)}\, du = \sin{\left(u \right)}$
        
        So, the result is: $\frac{\sin{\left(u \right)}}{2}$
        
        Now substitute $u$ back in:
        
        $\frac{\sin{\left(2 x \right)}}{2}$
      So, the result is: $- \frac{\sin{\left(2 x \right)}}{4}$
    The result is: $\frac{x}{2} - \frac{\sin{\left(2 x \right)}}{4}$
  So, the result is: $- 2 x + \sin{\left(2 x \right)}$
The result is: $\sin{\left(2 x \right)}$
Add the constant of integration:

$\sin{\left(2 x \right)}+ \mathrm{constant}$

The answer is:

$\sin{\left(2 x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                          
 |                           
 | sin(4*x)                  
 | -------- dx = C + sin(2*x)
 | sin(2*x)                  
 |                           
/

$$\int \frac{\sin{\left(4 x \right)}}{\sin{\left(2 x \right)}}\, dx = C + \sin{\left(2 x \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

sin(2)

$$\sin{\left(2 \right)}$$

sin(2)

$$\sin{\left(2 \right)}$$

sin(2)

Numerical answer [src]

0.909297426825682

0.909297426825682

The graph

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

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Identical expressions

Similar expressions

Integral of sin(4x)/sin(2x) dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sin(4*x)/sin(2*x) dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of sin(4x)/sin(2x) dx