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Solving integrals/ x*cos(x)/((2*dx))

Integral of x*cos(x)/((2*dx)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

    1. Use integration by parts:

      Let and let .

      Then .

      To find :

      1. The integral of cosine is sine:

      Now evaluate the sub-integral.

    2. The integral of sine is negative cosine:

    So, the result is:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                                    
 | x*cos(x)          cos(x)   x*sin(x)
 | -------- dx = C + ------ + --------
 |    2                2         2    
 |                                    
/
$$\int \frac{x \cos{\left(x \right)}}{2}\, dx = C + \frac{x \sin{\left(x \right)}}{2} + \frac{\cos{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
0
$$0$$ 
=
= 
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$$0$$ 
0
Numerical answer [src] 
0.0
0.0

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

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