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Solving integrals/ sin(x/4)dx

Integral of sin(x/4)dx dx

The solution

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

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

Detail solution

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

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

$\int 4 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sin{\left(u \right)}\, du = 4 \int \sin{\left(u \right)}\, du$
  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]

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

4 - 4*cos(1/4)

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

4 - 4*cos(1/4)

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

4 - 4*cos(1/4)

Numerical answer [src]

0.124350313157421

0.124350313157421

The graph

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

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Identical expressions

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Integral of sin(x/4)dx dx

Limits of integration:

The graph:

Piecewise:

The solution