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Solving integrals/ (x-4)

Integral of (x-4) dx

Limits of integration:

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Piecewise:

The solution

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-2
∫−24(x−4) dx\int\limits_{-2}^{4} \left(x - 4\right)\, dx 
Integral(x - 4, (x, -2, 4))
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:

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

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

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

    The result is: x22−4x\frac{x^{2}}{2} - 4 x

  2. Now simplify:

    x(x−8)2\frac{x \left(x - 8\right)}{2}

  3. Add the constant of integration:

    x(x−8)2+constant\frac{x \left(x - 8\right)}{2}+ \mathrm{constant}

The answer is:

x(x−8)2+constant\frac{x \left(x - 8\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  2      
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 | (x - 4) dx = C + -- - 4*x
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∫(x−4) dx=C+x22−4x\int \left(x - 4\right)\, dx = C + \frac{x^{2}}{2} - 4 x
Simplify
The graph
-2.0-1.5-1.0-0.54.00.00.51.01.52.02.53.03.5-2020
Plot the graph f(x)
The answer [src] 
-18
−18-18 
=
= 
-18
−18-18 
-18
Numerical answer [src] 
-18.0
-18.0

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

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