Integral of sin(x)*dx/2 dx

The solution

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

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

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

Detail solution

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

$\int \frac{\sin{\left(x \right)}}{2}\, dx = \frac{\int \sin{\left(x \right)}\, dx}{2}$
1. The integral of sine is negative cosine:
  
  $\int \sin{\left(x \right)}\, dx = - \cos{\left(x \right)}$
So, the result is: $- \frac{\cos{\left(x \right)}}{2}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                      
 |                       
 | sin(x)          cos(x)
 | ------ dx = C - ------
 |   2               2   
 |                       
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

1   cos(1)
- - ------
2     2

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

1   cos(1)
- - ------
2     2

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

1/2 - cos(1)/2

Numerical answer [src]

0.22984884706593

0.22984884706593

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)*dx/2 dx

Limits of integration:

The graph:

Piecewise:

The solution