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Solving integrals/ xyz

Integral of xyz dx

Limits of integration:

from to
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The graph:

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Piecewise:

The solution

You have entered [src] 
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 |  x*y*z dx
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∫01xyz dx\int\limits_{0}^{1} x y z\, dx 
Integral(x*y*z, (x, 0, 1))
Detail solution

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

    ∫xyz dx=yz∫x dx\int x y z\, dx = y z \int x\, dx

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

    So, the result is: x2yz2\frac{x^{2} y z}{2}

  2. Add the constant of integration:

    x2yz2+constant\frac{x^{2} y z}{2}+ \mathrm{constant}

The answer is:

x2yz2+constant\frac{x^{2} y z}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                    2
 |                y*z*x 
 | x*y*z dx = C + ------
 |                  2   
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∫xyz dx=C+x2yz2\int x y z\, dx = C + \frac{x^{2} y z}{2}
Simplify
The answer [src] 
y*z
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 2
yz2\frac{y z}{2} 
=
= 
y*z
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 2
yz2\frac{y z}{2}
Упростить

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

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