Integral of sin(x/2) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |     /x\   
 |  sin|-| dx
 |     \2/   
 |           
/            
0

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

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

Detail solution

Let $u = \frac{x}{2}$ .

Then let $du = \frac{dx}{2}$ and substitute $2 du$ :

$\int 4 \sin{\left(u \right)}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 \sin{\left(u \right)}\, du = 2 \int \sin{\left(u \right)}\, du$
  1. The integral of sine is negative cosine:
    
    $\int \sin{\left(u \right)}\, du = - \cos{\left(u \right)}$
  So, the result is: $- 2 \cos{\left(u \right)}$
Now substitute $u$ back in:

$- 2 \cos{\left(\frac{x}{2} \right)}$
Now simplify:

$- 2 \cos{\left(\frac{x}{2} \right)}$
Add the constant of integration:

$- 2 \cos{\left(\frac{x}{2} \right)}+ \mathrm{constant}$

The answer is:

$- 2 \cos{\left(\frac{x}{2} \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                        
 |                         
 |    /x\               /x\
 | sin|-| dx = C - 2*cos|-|
 |    \2/               \2/
 |                         
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

2 - 2*cos(1/2)

$$2 - 2 \cos{\left(\frac{1}{2} \right)}$$

2 - 2*cos(1/2)

$$2 - 2 \cos{\left(\frac{1}{2} \right)}$$

Упростить

Numerical answer [src]

0.244834876219255

0.244834876219255

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of sin(x/2) dx

Limits of integration:

The graph:

Piecewise:

The solution