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Solving integrals/ x^2-xdx

Integral of x^2-xdx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫01(x2−x) dx\int\limits_{0}^{1} \left(x^{2} - x\right)\, dx 
Integral(x^2 - x, (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    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}

    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}

    The result is: x33−x22\frac{x^{3}}{3} - \frac{x^{2}}{2}

  2. Now simplify:

    x2(2x−3)6\frac{x^{2} \left(2 x - 3\right)}{6}

  3. Add the constant of integration:

    x2(2x−3)6+constant\frac{x^{2} \left(2 x - 3\right)}{6}+ \mathrm{constant}

The answer is:

x2(2x−3)6+constant\frac{x^{2} \left(2 x - 3\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
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∫(x2−x) dx=C+x33−x22\int \left(x^{2} - x\right)\, dx = C + \frac{x^{3}}{3} - \frac{x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-0.500.25
Plot the graph f(x)
The answer [src] 
-1/6
−16- \frac{1}{6} 
=
= 
-1/6
−16- \frac{1}{6} 
-1/6
Numerical answer [src] 
-0.166666666666667
-0.166666666666667

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

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