Mister Exam

Integral of 2*x-1 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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01(2x1)dx\int\limits_{0}^{1} \left(2 x - 1\right)\, dx
Integral(2*x - 1, (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

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

      2xdx=2xdx\int 2 x\, 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: x2x^{2}

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

      (1)dx=x\int \left(-1\right)\, dx = - x

    The result is: x2xx^{2} - x

  2. Now simplify:

    x(x1)x \left(x - 1\right)

  3. Add the constant of integration:

    x(x1)+constantx \left(x - 1\right)+ \mathrm{constant}


The answer is:

x(x1)+constantx \left(x - 1\right)+ \mathrm{constant}

The answer (Indefinite) [src]
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(2x1)dx=C+x2x\int \left(2 x - 1\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 2*x-1 dx

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