Mister Exam

Other calculators

cosx/2
Solving integrals/ cosx/2

Integral of cosx/2 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |  cos(x)   
 |  ------ dx
 |    2      
 |           
/            
0
∫01cos⁡(x)2 dx\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{2}\, dx 
Integral(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:

    ∫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
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
sin(1)
------
  2
sin⁡(1)2\frac{\sin{\left(1 \right)}}{2} 
=
= 
sin(1)
------
  2
sin⁡(1)2\frac{\sin{\left(1 \right)}}{2} 
sin(1)/2
Numerical answer [src] 
0.420735492403948
0.420735492403948
The graph
Integral of cosx/2 dx

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

    © Mister Exam – Calculator