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

Integral of x^3-3*x^2 dx

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Piecewise:

The solution

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∫02(x3−3x2) dx\int\limits_{0}^{2} \left(x^{3} - 3 x^{2}\right)\, dx 
Integral(x^3 - 3*x^2, (x, 0, 2))
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:

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

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

        ∫3x2 dx=3∫x2 dx\int 3 x^{2}\, dx = 3 \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: x3x^{3}

      So, the result is: −x3- x^{3}

    The result is: x44−x3\frac{x^{4}}{4} - x^{3}

  2. Now simplify:

    x3(x−4)4\frac{x^{3} \left(x - 4\right)}{4}

  3. Add the constant of integration:

    x3(x−4)4+constant\frac{x^{3} \left(x - 4\right)}{4}+ \mathrm{constant}

The answer is:

x3(x−4)4+constant\frac{x^{3} \left(x - 4\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
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 | / 3      2\           3   x 
 | \x  - 3*x / dx = C - x  + --
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x44−x3{{x^4}\over{4}}-x^3
Simplify
The graph
0.02.00.20.40.60.81.01.21.41.61.85-5
Plot the graph f(x)
The answer [src] 
-4
−4-4 
=
= 
-4
−4-4
Simplify
Numerical answer [src] 
-4.0
-4.0
The graph
Integral of x^3-3*x^2 dx

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

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