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Integral of x-7 dx

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The solution

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∫01(x−7) dx\int\limits_{0}^{1} \left(x - 7\right)\, dx 
Integral(x - 7, (x, 0, 1))
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:

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

    The result is: x22−7x\frac{x^{2}}{2} - 7 x

  2. Now simplify:

    x(x−14)2\frac{x \left(x - 14\right)}{2}

  3. Add the constant of integration:

    x(x−14)2+constant\frac{x \left(x - 14\right)}{2}+ \mathrm{constant}

The answer is:

x(x−14)2+constant\frac{x \left(x - 14\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                  2      
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 | (x - 7) dx = C + -- - 7*x
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∫(x−7) dx=C+x22−7x\int \left(x - 7\right)\, dx = C + \frac{x^{2}}{2} - 7 x
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1010
Plot the graph f(x)
The answer [src] 
-13/2
−132- \frac{13}{2} 
=
= 
-13/2
−132- \frac{13}{2} 
-13/2
Numerical answer [src] 
-6.5
-6.5
The graph
Integral of x-7 dx

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

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