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Solving integrals/ x*y*z/((3*m))

Integral of x*y*z/((3*m)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |  x*y*z   
 |  ----- dx
 |   3*m    
 |          
/           
0
$$\int\limits_{0}^{1} \frac{z x y}{3 m}\, dx$$ 
Integral(((x*y)*z)/((3*m)), (x, 0, 1))
Detail solution

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

    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:

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                    2  1 
 |                y*z*x *---
 | x*y*z                 3*m
 | ----- dx = C + ----------
 |  3*m               2     
 |                          
/
$$\int \frac{z x y}{3 m}\, dx = C + \frac{\frac{1}{3 m} x^{2} y z}{2}$$
Simplify
The answer [src] 
y*z
---
6*m
$$\frac{y z}{6 m}$$ 
=
= 
y*z
---
6*m
$$\frac{y z}{6 m}$$ 
y*z/(6*m)

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

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