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Solving integrals/ x*y

Integral of x*y dx

Limits of integration:

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Piecewise:

The solution

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

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

    ∫xy dx=y∫x dx\int x y\, dx = y \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: x2y2\frac{x^{2} y}{2}

  2. Add the constant of integration:

    x2y2+constant\frac{x^{2} y}{2}+ \mathrm{constant}

The answer is:

x2y2+constant\frac{x^{2} y}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                2
 |              y*x 
 | x*y dx = C + ----
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x2 y2{{x^2\,y}\over{2}}
Simplify
The answer [src] 
y
-
2
y2{{y}\over{2}} 
=
= 
y
-
2
y2\frac{y}{2}
Упростить

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

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