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Integral of x^3-27 dx

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The solution

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03(x327)dx\int\limits_{0}^{3} \left(x^{3} - 27\right)\, dx
Integral(x^3 - 27, (x, 0, 3))
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:

      x3dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

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

      (27)dx=27x\int \left(-27\right)\, dx = - 27 x

    The result is: x4427x\frac{x^{4}}{4} - 27 x

  2. Now simplify:

    x(x3108)4\frac{x \left(x^{3} - 108\right)}{4}

  3. Add the constant of integration:

    x(x3108)4+constant\frac{x \left(x^{3} - 108\right)}{4}+ \mathrm{constant}


The answer is:

x(x3108)4+constant\frac{x \left(x^{3} - 108\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src]
  /                            
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 | \x  - 27/ dx = C - 27*x + --
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(x327)dx=C+x4427x\int \left(x^{3} - 27\right)\, dx = C + \frac{x^{4}}{4} - 27 x
The graph
0.003.000.250.500.751.001.251.501.752.002.252.502.75-10050
The answer [src]
-243/4
2434- \frac{243}{4}
=
=
-243/4
2434- \frac{243}{4}
-243/4
Numerical answer [src]
-60.75
-60.75

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