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x*cos*x/2
Solving integrals/ x*cos*x/2

Integral of x*cos*x/2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |  x*cos(x)   
 |  -------- dx
 |     2       
 |             
/              
0
$$\int\limits_{0}^{1} \frac{x \cos{\left(x \right)}}{2}\, dx$$ 
Integral((x*cos(x))/2, (x, 0, 1))
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] 
  1   cos(1)   sin(1)
- - + ------ + ------
  2     2        2
$$- \frac{1}{2} + \frac{\cos{\left(1 \right)}}{2} + \frac{\sin{\left(1 \right)}}{2}$$ 
=
= 
  1   cos(1)   sin(1)
- - + ------ + ------
  2     2        2
$$- \frac{1}{2} + \frac{\cos{\left(1 \right)}}{2} + \frac{\sin{\left(1 \right)}}{2}$$ 
-1/2 + cos(1)/2 + sin(1)/2
Numerical answer [src] 
0.190886645338018
0.190886645338018
The graph
Integral of x*cos*x/2 dx

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

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