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Solving integrals/ 0.5*cos(x)

Integral of 0.5*cos(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -asin(4/5)         
      /             
     |              
     |     cos(x)   
     |     ------ dx
     |       2      
     |              
    /               
   -pi              
   ----             
    2
∫−π2−asin⁡(45)cos⁡(x)2 dx\int\limits_{- \frac{\pi}{2}}^{- \operatorname{asin}{\left(\frac{4}{5} \right)}} \frac{\cos{\left(x \right)}}{2}\, dx 
Integral(cos(x)/2, (x, -pi/2, -asin(4/5)))
Detail solution

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

    ∫cos⁡(x)2 dx=∫cos⁡(x) dx2\int \frac{\cos{\left(x \right)}}{2}\, dx = \frac{\int \cos{\left(x \right)}\, dx}{2}

    1. The integral of cosine is sine:

      ∫cos⁡(x) dx=sin⁡(x)\int \cos{\left(x \right)}\, dx = \sin{\left(x \right)}

    So, the result is: sin⁡(x)2\frac{\sin{\left(x \right)}}{2}

  2. Add the constant of integration:

    sin⁡(x)2+constant\frac{\sin{\left(x \right)}}{2}+ \mathrm{constant}

The answer is:

sin⁡(x)2+constant\frac{\sin{\left(x \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                      
 |                       
 | cos(x)          sin(x)
 | ------ dx = C + ------
 |   2               2   
 |                       
/
∫cos⁡(x)2 dx=C+sin⁡(x)2\int \frac{\cos{\left(x \right)}}{2}\, dx = C + \frac{\sin{\left(x \right)}}{2}
Simplify
The graph
-1.55-1.50-1.45-1.40-1.35-1.30-1.25-1.20-1.15-1.10-1.05-1.00-0.951.0-1.0
Plot the graph f(x)
The answer [src] 
1/10
110\frac{1}{10} 
=
= 
1/10
110\frac{1}{10} 
1/10
Numerical answer [src] 
0.1
0.1

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

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