Integral of sen(x/4)dx dx

The solution

You have entered [src]

 POST_GRBEK_SMALL_pi           
          /                    
         |                     
         |             /x\     
         |          sin|-|*1 dx
         |             \4/     
         |                     
        /                      
        0

$$\int\limits_{0}^{POST_{GRBEK SMALL \pi}} \sin{\left(\frac{x}{4} \right)} 1\, dx$$

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

Detail solution

Let $u = \frac{x}{4}$ .

Then let $du = \frac{dx}{4}$ and substitute $4 du$ :

$\int 16 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 4 \sin{\left(u \right)}\, du = 4 \int \sin{\left(u \right)}\, du$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- 4 \cos{\left(u \right)}$
Now substitute $u$ back in:

$- 4 \cos{\left(\frac{x}{4} \right)}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                          
 |                           
 |    /x\                 /x\
 | sin|-|*1 dx = C - 4*cos|-|
 |    \4/                 \4/
 |                           
/

$$-4\,\cos \left({{x}\over{4}}\right)$$

Simplify

The answer [src]

         /POST_GRBEK_SMALL_pi\
4 - 4*cos|-------------------|
         \         4         /

$$4 - 4 \cos{\left(\frac{POST_{GRBEK SMALL \pi}}{4} \right)}$$

         /POST_GRBEK_SMALL_pi\
4 - 4*cos|-------------------|
         \         4         /

$$4 - 4 \cos{\left(\frac{POST_{GRBEK SMALL \pi}}{4} \right)}$$

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

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Identical expressions

Integral of sen(x/4)dx dx

Limits of integration:

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The solution