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x^3-2x^2
Solving integrals/ x^3-2x^2

Integral of x^3-2x^2 dx

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The solution

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∫01(x3−2x2) dx\int\limits_{0}^{1} \left(x^{3} - 2 x^{2}\right)\, dx 
Integral(x^3 - 2*x^2, (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:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

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

      ∫(−2x2) dx=−2∫x2 dx\int \left(- 2 x^{2}\right)\, dx = - 2 \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: −2x33- \frac{2 x^{3}}{3}

    The result is: x44−2x33\frac{x^{4}}{4} - \frac{2 x^{3}}{3}

  2. Now simplify:

    x3(3x−8)12\frac{x^{3} \left(3 x - 8\right)}{12}

  3. Add the constant of integration:

    x3(3x−8)12+constant\frac{x^{3} \left(3 x - 8\right)}{12}+ \mathrm{constant}

The answer is:

x3(3x−8)12+constant\frac{x^{3} \left(3 x - 8\right)}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                              
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 | \x  - 2*x / dx = C - ---- + --
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∫(x3−2x2) dx=C+x44−2x33\int \left(x^{3} - 2 x^{2}\right)\, dx = C + \frac{x^{4}}{4} - \frac{2 x^{3}}{3}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.901-2
Plot the graph f(x)
The answer [src] 
-5/12
−512- \frac{5}{12} 
=
= 
-5/12
−512- \frac{5}{12} 
-5/12
Numerical answer [src] 
-0.416666666666667
-0.416666666666667
The graph
Integral of x^3-2x^2 dx

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

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