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x^2-7x+6
Solving integrals/ x^2-7x+6

Integral of x^2-7x+6 dx

Limits of integration:

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The solution

You have entered [src] 
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∫01(x2−7x+6) dx\int\limits_{0}^{1} \left(x^{2} - 7 x + 6\right)\, dx
Simplify
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:

      ∫(−7x) dx=−∫7x dx\int \left(- 7 x\right)\, dx = - \int 7 x\, dx

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

        ∫7x dx=7∫x dx\int 7 x\, dx = 7 \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: 7x22\frac{7 x^{2}}{2}

      So, the result is: −7x22- \frac{7 x^{2}}{2}

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

      ∫6 dx=6x\int 6\, dx = 6 x

    The result is: x33−7x22+6x\frac{x^{3}}{3} - \frac{7 x^{2}}{2} + 6 x

  2. Now simplify:

    x(2x2−21x+36)6\frac{x \left(2 x^{2} - 21 x + 36\right)}{6}

  3. Add the constant of integration:

    x(2x2−21x+36)6+constant\frac{x \left(2 x^{2} - 21 x + 36\right)}{6}+ \mathrm{constant}

The answer is:

x(2x2−21x+36)6+constant\frac{x \left(2 x^{2} - 21 x + 36\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                       
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 | \x  - 7*x + 6/ dx = C + 6*x - ---- + --
 |                                2     3 
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x33−7 x22+6 x{{x^3}\over{3}}-{{7\,x^2}\over{2}}+6\,x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90010
Plot the graph f(x)
The answer [src] 
17/6
176{{17}\over{6}} 
=
= 
17/6
176\frac{17}{6}
Simplify
Numerical answer [src] 
2.83333333333333
2.83333333333333
The graph
Integral of x^2-7x+6 dx

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

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