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

Integral of -x^2-x dx

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The solution

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∫01(−x2−x) dx\int\limits_{0}^{1} \left(- x^{2} - x\right)\, dx 
Integral(-x^2 - x, (x, 0, 1))
Detail solution

  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:

      ∫(−x) dx=−∫x dx\int \left(- x\right)\, dx = - \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: −x22- \frac{x^{2}}{2}

    The result is: −x33−x22- \frac{x^{3}}{3} - \frac{x^{2}}{2}

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(−x2−x) dx=C−x33−x22\int \left(- x^{2} - x\right)\, dx = C - \frac{x^{3}}{3} - \frac{x^{2}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-4
Plot the graph f(x)
The answer [src] 
-5/6
−56- \frac{5}{6} 
=
= 
-5/6
−56- \frac{5}{6} 
-5/6
Numerical answer [src] 
-0.833333333333333
-0.833333333333333
The graph
Integral of -x^2-x dx

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

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