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

Integral of x^2-4x+4 dx

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The solution

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

      ∫4 dx=4x\int 4\, dx = 4 x

    The result is: x33−2x2+4x\frac{x^{3}}{3} - 2 x^{2} + 4 x

  2. Now simplify:

    x(x2−6x+12)3\frac{x \left(x^{2} - 6 x + 12\right)}{3}

  3. Add the constant of integration:

    x(x2−6x+12)3+constant\frac{x \left(x^{2} - 6 x + 12\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−6x+12)3+constant\frac{x \left(x^{2} - 6 x + 12\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  - 4*x + 4/ dx = C - 2*x  + 4*x + --
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∫((x2−4x)+4) dx=C+x33−2x2+4x\int \left(\left(x^{2} - 4 x\right) + 4\right)\, dx = C + \frac{x^{3}}{3} - 2 x^{2} + 4 x
Simplify
The graph
1.002.001.101.201.301.401.501.601.701.801.900.05.0
Plot the graph f(x)
The answer [src] 
1/3
13\frac{1}{3} 
=
= 
1/3
13\frac{1}{3} 
1/3
Numerical answer [src] 
0.333333333333333
0.333333333333333
The graph
Integral of x^2-4x+4 dx

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

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