Mister Exam

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Identical expressions
x*y*z/((three *m))
x multiply by y multiply by z divide by ((3 multiply by m))
x multiply by y multiply by z divide by ((three multiply by m))
xyz/((3m))
xyz/3m
x*y*z divide by ((3*m))
x*y*z/((3*m))dx

Integral of xyz/((3*m)) dx

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

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

$\int \frac{z x y}{3 m}\, dx = \frac{1}{3 m} \int x y z\, dx$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int x y z\, dx = y z \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{x^{2} y z}{2}$
So, the result is: $\frac{\frac{1}{3 m} x^{2} y z}{2}$
Now simplify:

$\frac{x^{2} y z}{6 m}$
Add the constant of integration:

$\frac{x^{2} y z}{6 m}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} y z}{6 m}+ \mathrm{constant}$

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.

Other calculators

How to use it?

Identical expressions

Integral of xyz/((3*m)) dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

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

Limits of integration:

The graph:

Piecewise:

The solution

Integral of xyz/((3*m)) dx