Mister Exam

Integral of x-3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

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01(x3)dx\int\limits_{0}^{1} \left(x - 3\right)\, dx
Integral(x - 3, (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 n1n \neq -1:

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

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

      (3)dx=3x\int \left(-3\right)\, dx = - 3 x

    The result is: x223x\frac{x^{2}}{2} - 3 x

  2. Now simplify:

    x(x6)2\frac{x \left(x - 6\right)}{2}

  3. Add the constant of integration:

    x(x6)2+constant\frac{x \left(x - 6\right)}{2}+ \mathrm{constant}


The answer is:

x(x6)2+constant\frac{x \left(x - 6\right)}{2}+ \mathrm{constant}

The answer (Indefinite) [src]
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(x3)dx=C+x223x\int \left(x - 3\right)\, dx = C + \frac{x^{2}}{2} - 3 x
The graph
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The answer [src]
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Numerical answer [src]
-2.5
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The graph
Integral of x-3 dx

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