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x²-4x
Solving integrals/ x²-4x

Integral of x²-4x dx

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The solution

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∫01(x2−4x) dx\int\limits_{0}^{1} \left(x^{2} - 4 x\right)\, dx 
Integral(x^2 - 4*x, (x, 0, 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:

      ∫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=−∫4x dx\int \left(- 4 x\right)\, dx = - \int 4 x\, dx

      1. The integral of a constant times a function is the constant times the integral of the function:

        ∫4x dx=4∫x dx\int 4 x\, 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: 2x22 x^{2}

      So, the result is: −2x2- 2 x^{2}

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

  2. Now simplify:

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

  3. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
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∫(x2−4x) dx=C+x33−2x2\int \left(x^{2} - 4 x\right)\, dx = C + \frac{x^{3}}{3} - 2 x^{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.905-5
Plot the graph f(x)
The answer [src] 
-5/3
−53- \frac{5}{3} 
=
= 
-5/3
−53- \frac{5}{3}
Упростить
Numerical answer [src] 
-1.66666666666667
-1.66666666666667
The graph
Integral of x²-4x dx

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

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