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Solving integrals/ yx^2

Integral of yx^2 dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

You have entered [src] 
  1        
  /        
 |         
 |     2   
 |  y*x  dx
 |         
/          
0
∫01x2y dx\int\limits_{0}^{1} x^{2} y\, dx
Simplify
Detail solution

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

    ∫x2y dx=y∫x2 dx\int x^{2} y\, dx = y \int x^{2}\, dx

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

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

    So, the result is: x3y3\frac{x^{3} y}{3}

  2. Add the constant of integration:

    x3y3+constant\frac{x^{3} y}{3}+ \mathrm{constant}

The answer is:

x3y3+constant\frac{x^{3} y}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  
 |                  3
 |    2          y*x 
 | y*x  dx = C + ----
 |                3  
/
x3 y3{{x^3\,y}\over{3}}
Simplify
The answer [src] 
y
-
3
y3{{y}\over{3}} 
=
= 
y
-
3
y3\frac{y}{3}
Simplify

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

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