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

Integral of x^3-x^2 dx

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The solution

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

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

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

  2. Now simplify:

    x3⋅(3x−4)12\frac{x^{3} \cdot \left(3 x - 4\right)}{12}

  3. Add the constant of integration:

    x3⋅(3x−4)12+constant\frac{x^{3} \cdot \left(3 x - 4\right)}{12}+ \mathrm{constant}

The answer is:

x3⋅(3x−4)12+constant\frac{x^{3} \cdot \left(3 x - 4\right)}{12}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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 | \x  - x / dx = C - -- + --
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∫(x3−x2) dx=C+x44−x33\int \left(x^{3} - x^{2}\right)\, dx = C + \frac{x^{4}}{4} - \frac{x^{3}}{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] 
4/3
43\frac{4}{3} 
=
= 
4/3
43\frac{4}{3}
Упростить
Numerical answer [src] 
1.33333333333333
1.33333333333333
The graph
Integral of x^3-x^2 dx

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

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