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x^3-3x^2+1
Solving integrals/ x^3-3x^2+1

Integral of x^3-3x^2+1 dx

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The solution

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∫−11(x3−3x2+1) dx\int\limits_{-1}^{1} \left(x^{3} - 3 x^{2} + 1\right)\, dx 
Integral(x^3 - 3*x^2 + 1, (x, -1, 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:

      ∫(−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}

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

      ∫1 dx=x\int 1\, dx = x

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

  2. Add the constant of integration:

    x44−x3+x+constant\frac{x^{4}}{4} - x^{3} + x+ \mathrm{constant}

The answer is:

x44−x3+x+constant\frac{x^{4}}{4} - x^{3} + x+ \mathrm{constant}

The answer (Indefinite) [src] 
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x44−x3+x{{x^4}\over{4}}-x^3+x
Simplify
The graph
-1.0-0.8-0.6-0.4-0.21.00.00.20.40.60.85-5
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The answer [src] 
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Numerical answer [src] 
5.62837573394741e-19
5.62837573394741e-19
The graph
Integral of x^3-3x^2+1 dx

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

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