Mister Exam

Integral of (x-y) dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1           
  /           
 |            
 |  (x - y) dy
 |            
/             
-1            
$$\int\limits_{-1}^{1} \left(x - y\right)\, dy$$
Integral(x - y, (y, -1, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

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

      1. The integral of is when :

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                  2      
 |                  y       
 | (x - y) dy = C - -- + x*y
 |                  2       
/                           
$$x\,y-{{y^2}\over{2}}$$
The answer [src]
2*x
$${{2\,x+1}\over{2}}+{{2\,x-1}\over{2}}$$
=
=
2*x
$$2 x$$

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