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Solving integrals/ x^2-x+4

Integral of x^2-x+4 dx

Limits of integration:

from to
v

The graph:

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Piecewise:

The solution

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

        ∫(−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}

    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−x22+4x\frac{x^{3}}{3} - \frac{x^{2}}{2} + 4 x

  2. Now simplify:

    x(2x2−3x+24)6\frac{x \left(2 x^{2} - 3 x + 24\right)}{6}

  3. Add the constant of integration:

    x(2x2−3x+24)6+constant\frac{x \left(2 x^{2} - 3 x + 24\right)}{6}+ \mathrm{constant}

The answer is:

x(2x2−3x+24)6+constant\frac{x \left(2 x^{2} - 3 x + 24\right)}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                   
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 | \x  - x + 4/ dx = C + 4*x - -- + --
 |                             2    3 
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∫((x2−x)+4) dx=C+x33−x22+4x\int \left(\left(x^{2} - x\right) + 4\right)\, dx = C + \frac{x^{3}}{3} - \frac{x^{2}}{2} + 4 x
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.75-1010
Plot the graph f(x)
The answer [src] 
27/2
272\frac{27}{2} 
=
= 
27/2
272\frac{27}{2} 
27/2
Numerical answer [src] 
13.5
13.5

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

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