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Solving integrals/ 0.5cos(x)x

Integral of 0.5cos(x)x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi            
 --            
 4             
  /            
 |             
 |  cos(x)     
 |  ------*x dx
 |    2        
 |             
/              
0
$$\int\limits_{0}^{\frac{\pi}{4}} x \frac{\cos{\left(x \right)}}{2}\, dx$$ 
Integral((cos(x)/2)*x, (x, 0, pi/4))
The answer (Indefinite) [src] 
  /                                   
 |                                    
 | cos(x)            cos(x)   x*sin(x)
 | ------*x dx = C + ------ + --------
 |   2                 2         2    
 |                                    
/
$$\int x \frac{\cos{\left(x \right)}}{2}\, dx = C + \frac{x \sin{\left(x \right)}}{2} + \frac{\cos{\left(x \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ___        ___
  1   \/ 2    pi*\/ 2 
- - + ----- + --------
  2     4        16
$$- \frac{1}{2} + \frac{\sqrt{2} \pi}{16} + \frac{\sqrt{2}}{4}$$ 
=
= 
        ___        ___
  1   \/ 2    pi*\/ 2 
- - + ----- + --------
  2     4        16
$$- \frac{1}{2} + \frac{\sqrt{2} \pi}{16} + \frac{\sqrt{2}}{4}$$ 
-1/2 + sqrt(2)/4 + pi*sqrt(2)/16
Numerical answer [src] 
0.131233574228172
0.131233574228172

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

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