Mister Exam

Integral of cos0,5x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 5*pi             
 ----             
  3               
   /              
  |               
  |  cos(0.5*x) dx
  |               
 /                
3*pi              
$$\int\limits_{3 \pi}^{\frac{5 \pi}{3}} \cos{\left(0.5 x \right)}\, dx$$
Integral(cos(0.5*x), (x, 3*pi, 5*pi/3))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. The integral of cosine is sine:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                  
 |                                   
 | cos(0.5*x) dx = C + 2.0*sin(0.5*x)
 |                                   
/                                    
$$\int \cos{\left(0.5 x \right)}\, dx = C + 2.0 \sin{\left(0.5 x \right)}$$
The graph
The answer [src]
2.0 + 2.0*sin(0.833333333333333*pi)
$$2.0 \sin{\left(0.833333333333333 \pi \right)} + 2.0$$
=
=
2.0 + 2.0*sin(0.833333333333333*pi)
$$2.0 \sin{\left(0.833333333333333 \pi \right)} + 2.0$$
2.0 + 2.0*sin(0.833333333333333*pi)
Numerical answer [src]
3.0
3.0

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