Mister Exam

Other calculators

Solving integrals/ sin((x-y)/2)

Integral of sin((x-y)/2) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 2*pi             
   /              
  |               
  |     /x - y\   
  |  sin|-----| dy
  |     \  2  /   
  |               
 /                
 0
$$\int\limits_{0}^{2 \pi} \sin{\left(\frac{x - y}{2} \right)}\, dy$$ 
Integral(sin((x - y)/2), (y, 0, 2*pi))
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 sine is negative cosine:

      So, the result is:

    Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                
 |                                 
 |    /x - y\               /x - y\
 | sin|-----| dy = C + 2*cos|-----|
 |    \  2  /               \  2  /
 |                                 
/
$$\int \sin{\left(\frac{x - y}{2} \right)}\, dy = C + 2 \cos{\left(\frac{x - y}{2} \right)}$$
Simplify
The answer [src] 
      /x\
-4*cos|-|
      \2/
$$- 4 \cos{\left(\frac{x}{2} \right)}$$ 
=
= 
      /x\
-4*cos|-|
      \2/
$$- 4 \cos{\left(\frac{x}{2} \right)}$$ 
-4*cos(x/2)

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

    © Mister Exam – Calculator