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Solving integrals/ x^3-27

Integral of x^3-27 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
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0
∫03(x3−27) 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 n≠−1n \neq -1:

      ∫x3 dx=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: x44−27x\frac{x^{4}}{4} - 27 x

  2. Now simplify:

    x(x3−108)4\frac{x \left(x^{3} - 108\right)}{4}

  3. Add the constant of integration:

    x(x3−108)4+constant\frac{x \left(x^{3} - 108\right)}{4}+ \mathrm{constant}

The answer is:

x(x3−108)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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∫(x3−27) dx=C+x44−27x\int \left(x^{3} - 27\right)\, dx = C + \frac{x^{4}}{4} - 27 x
Simplify
The graph
0.003.000.250.500.751.001.251.501.752.002.252.502.75-10050
Plot the graph f(x)
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.

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