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Solving integrals/ (x2-x)dx

Integral of (x2-x)dx dx

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The solution

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  2            
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∫12(−x+x2) dx\int\limits_{1}^{2} \left(- x + x_{2}\right)\, dx 
Integral(x2 - x, (x, 1, 2))
Detail solution

  1. Integrate term-by-term:

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

      ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \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: −x22- \frac{x^{2}}{2}

    1. The integral of a constant is the constant times the variable of integration:

      ∫x2 dx=xx2\int x_{2}\, dx = x x_{2}

    The result is: −x22+xx2- \frac{x^{2}}{2} + x x_{2}

  2. Now simplify:

    x(−x+2x2)2\frac{x \left(- x + 2 x_{2}\right)}{2}

  3. Add the constant of integration:

    x(−x+2x2)2+constant\frac{x \left(- x + 2 x_{2}\right)}{2}+ \mathrm{constant}

The answer is:

x(−x+2x2)2+constant\frac{x \left(- x + 2 x_{2}\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                   2       
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∫(−x+x2) dx=C−x22+xx2\int \left(- x + x_{2}\right)\, dx = C - \frac{x^{2}}{2} + x x_{2}
Simplify
The answer [src] 
-3/2 + x2
x2−32x_{2} - \frac{3}{2} 
=
= 
-3/2 + x2
x2−32x_{2} - \frac{3}{2} 
-3/2 + x2

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

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