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Solving integrals/ x^2-4x-2

Integral of x^2-4x-2 dx

Limits of integration:

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Piecewise:

The solution

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∫−12((x2−4x)−2) dx\int\limits_{-1}^{2} \left(\left(x^{2} - 4 x\right) - 2\right)\, dx 
Integral(x^2 - 4*x - 2, (x, -1, 2))
Detail solution

  1. Integrate term-by-term:

    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:

        ∫(−4x) dx=−4∫x dx\int \left(- 4 x\right)\, dx = - 4 \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: −2x2- 2 x^{2}

      The result is: x33−2x2\frac{x^{3}}{3} - 2 x^{2}

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

      ∫(−2) dx=−2x\int \left(-2\right)\, dx = - 2 x

    The result is: x33−2x2−2x\frac{x^{3}}{3} - 2 x^{2} - 2 x

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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 | \x  - 4*x - 2/ dx = C - 2*x - 2*x  + --
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∫((x2−4x)−2) dx=C+x33−2x2−2x\int \left(\left(x^{2} - 4 x\right) - 2\right)\, dx = C + \frac{x^{3}}{3} - 2 x^{2} - 2 x
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.75-1010
Plot the graph f(x)
The answer [src] 
-9
−9-9 
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-9
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-9
Numerical answer [src] 
-9.0
-9.0

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

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