Mister Exam

Integral of x+y+z dy

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1               
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 |  (x + y + z) dy
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$$\int\limits_{0}^{1} \left(z + \left(x + y\right)\right)\, dy$$
Integral(x + y + z, (y, 0, 1))
Detail solution
  1. Integrate term-by-term:

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

    1. Integrate term-by-term:

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

      1. The integral of is when :

      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 + z) dy = C + -- + x*y + y*z
 |                      2             
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$$\int \left(z + \left(x + y\right)\right)\, dy = C + x y + \frac{y^{2}}{2} + y z$$
The answer [src]
1/2 + x + z
$$x + z + \frac{1}{2}$$
=
=
1/2 + x + z
$$x + z + \frac{1}{2}$$
1/2 + x + z

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