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Solving integrals/ 0,136*x*y

Integral of 0,136*x*y dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
 4 - y         
   /           
  |            
  |   17*x*y   
  |   ------ dx
  |    125     
  |            
 /             
 y             
 -             
 3
∫y34−y17xy125 dx\int\limits_{\frac{y}{3}}^{4 - y} \frac{17 x y}{125}\, dx 
Integral(17*x*y/125, (x, y/3, 4 - y))
Detail solution

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

    ∫17xy125 dx=17y∫x dx125\int \frac{17 x y}{125}\, dx = \frac{17 y \int x\, dx}{125}

    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: 17x2y250\frac{17 x^{2} y}{250}

  2. Add the constant of integration:

    17x2y250+constant\frac{17 x^{2} y}{250}+ \mathrm{constant}

The answer is:

17x2y250+constant\frac{17 x^{2} y}{250}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                       
 |                       2
 | 17*x*y          17*y*x 
 | ------ dx = C + -------
 |  125              250  
 |                        
/
17 x2 y250{{17\,x^2\,y}\over{250}}
Simplify
The answer [src] 
      3               2
  17*y    17*y*(4 - y) 
- ----- + -------------
   2250        250
17 y (y2−8 y+162−y218)125{{17\,y\,\left({{y^2-8\,y+16}\over{2}}-{{y^2}\over{18}}\right) }\over{125}} 
=
= 
      3               2
  17*y    17*y*(4 - y) 
- ----- + -------------
   2250        250
−17y32250+17y(4−y)2250- \frac{17 y^{3}}{2250} + \frac{17 y \left(4 - y\right)^{2}}{250}
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    Use the examples entering the upper and lower limits of integration.

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