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1-2*x

Integral of 1-2*x dx

Limits of integration:

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The solution

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01(12x)dx\int\limits_{0}^{1} \left(1 - 2 x\right)\, dx
Integral(1 - 2*x, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

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

      1dx=x\int 1\, dx = x

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

      (2x)dx=2xdx\int \left(- 2 x\right)\, dx = - 2 \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n1n \neq -1:

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

      So, the result is: x2- x^{2}

    The result is: x2+x- x^{2} + x

  2. Now simplify:

    x(1x)x \left(1 - x\right)

  3. Add the constant of integration:

    x(1x)+constantx \left(1 - x\right)+ \mathrm{constant}


The answer is:

x(1x)+constantx \left(1 - x\right)+ \mathrm{constant}

The answer (Indefinite) [src]
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(12x)dx=Cx2+x\int \left(1 - 2 x\right)\, dx = C - x^{2} + x
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
The answer [src]
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Numerical answer [src]
-1.25802354357785e-23
-1.25802354357785e-23
The graph
Integral of 1-2*x dx

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