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Solving integrals/ x*1/2*sin(x)

Integral of x*1/2*sin(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 157           
 ---           
  50           
  /            
 |             
 |  x          
 |  -*sin(x) dx
 |  2          
 |             
/              
0
$$\int\limits_{0}^{\frac{157}{50}} \frac{x}{2} \sin{\left(x \right)}\, dx$$ 
Integral((x/2)*sin(x), (x, 0, 157/50))
Detail solution

  1. Use integration by parts:

    Let and let .

    Then .

    To find :

    1. The integral of sine is negative cosine:

    Now evaluate the sub-integral.

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

    1. The integral of cosine is sine:

    So, the result is:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                                    
 | x                 sin(x)   x*cos(x)
 | -*sin(x) dx = C + ------ - --------
 | 2                   2         2    
 |                                    
/
$$\int \frac{x}{2} \sin{\left(x \right)}\, dx = C - \frac{x \cos{\left(x \right)}}{2} + \frac{\sin{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
   /157\          /157\
sin|---|   157*cos|---|
   \ 50/          \ 50/
-------- - ------------
   2           100
$$\frac{\sin{\left(\frac{157}{50} \right)}}{2} - \frac{157 \cos{\left(\frac{157}{50} \right)}}{100}$$ 
=
= 
   /157\          /157\
sin|---|   157*cos|---|
   \ 50/          \ 50/
-------- - ------------
   2           100
$$\frac{\sin{\left(\frac{157}{50} \right)}}{2} - \frac{157 \cos{\left(\frac{157}{50} \right)}}{100}$$ 
sin(157/50)/2 - 157*cos(157/50)/100
Numerical answer [src] 
1.57079433527048
1.57079433527048

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

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