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Solving integrals/ -x^2-4x-3

Integral of -x^2-4x-3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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-3
∫−3−1((−x2−4x)−3) dx\int\limits_{-3}^{-1} \left(\left(- x^{2} - 4 x\right) - 3\right)\, dx 
Integral(-x^2 - 4*x - 3, (x, -3, -1))
Detail solution

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      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}

      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:

      ∫(−3) dx=−3x\int \left(-3\right)\, dx = - 3 x

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

  2. Now simplify:

    −x(x2+6x+9)3- \frac{x \left(x^{2} + 6 x + 9\right)}{3}

  3. Add the constant of integration:

    −x(x2+6x+9)3+constant- \frac{x \left(x^{2} + 6 x + 9\right)}{3}+ \mathrm{constant}

The answer is:

−x(x2+6x+9)3+constant- \frac{x \left(x^{2} + 6 x + 9\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                         
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 | /   2          \                   2   x 
 | \- x  - 4*x - 3/ dx = C - 3*x - 2*x  - --
 |                                        3 
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∫((−x2−4x)−3) dx=C−x33−2x2−3x\int \left(\left(- x^{2} - 4 x\right) - 3\right)\, dx = C - \frac{x^{3}}{3} - 2 x^{2} - 3 x
Simplify
The graph
-3.0-1.0-2.8-2.6-2.4-2.2-2.0-1.8-1.6-1.4-1.202
Plot the graph f(x)
The answer [src] 
4/3
43\frac{4}{3} 
=
= 
4/3
43\frac{4}{3} 
4/3
Numerical answer [src] 
1.33333333333333
1.33333333333333

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

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