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Solving integrals/ x^2-6x+7

Integral of x^2-6x+7 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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∫−10−1((x2−6x)+7) dx\int\limits_{-10}^{-1} \left(\left(x^{2} - 6 x\right) + 7\right)\, dx 
Integral(x^2 - 6*x + 7, (x, -10, -1))
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:

        ∫(−6x) dx=−6∫x dx\int \left(- 6 x\right)\, dx = - 6 \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: −3x2- 3 x^{2}

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

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

      ∫7 dx=7x\int 7\, dx = 7 x

    The result is: x33−3x2+7x\frac{x^{3}}{3} - 3 x^{2} + 7 x

  2. Now simplify:

    x(x2−9x+21)3\frac{x \left(x^{2} - 9 x + 21\right)}{3}

  3. Add the constant of integration:

    x(x2−9x+21)3+constant\frac{x \left(x^{2} - 9 x + 21\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−9x+21)3+constant\frac{x \left(x^{2} - 9 x + 21\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
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 | \x  - 6*x + 7/ dx = C - 3*x  + 7*x + --
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∫((x2−6x)+7) dx=C+x33−3x2+7x\int \left(\left(x^{2} - 6 x\right) + 7\right)\, dx = C + \frac{x^{3}}{3} - 3 x^{2} + 7 x
Simplify
The graph
-1.0-9.0-8.0-7.0-6.0-5.0-4.0-3.0-2.0-10.0-10001000
Plot the graph f(x)
The answer [src] 
693
693693 
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= 
693
693693 
693
Numerical answer [src] 
693.0
693.0

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

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