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Solving integrals/ x^3-8

Integral of x^3-8 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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∫−12(x3−8) dx\int\limits_{-1}^{2} \left(x^{3} - 8\right)\, dx 
Integral(x^3 - 8, (x, -1, 2))
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:

      ∫(−8) dx=−8x\int \left(-8\right)\, dx = - 8 x

    The result is: x44−8x\frac{x^{4}}{4} - 8 x

  2. Now simplify:

    x(x3−32)4\frac{x \left(x^{3} - 32\right)}{4}

  3. Add the constant of integration:

    x(x3−32)4+constant\frac{x \left(x^{3} - 32\right)}{4}+ \mathrm{constant}

The answer is:

x(x3−32)4+constant\frac{x \left(x^{3} - 32\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                          
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∫(x3−8) dx=C+x44−8x\int \left(x^{3} - 8\right)\, dx = C + \frac{x^{4}}{4} - 8 x
Simplify
The graph
-1.00-0.75-0.50-0.252.000.000.250.500.751.001.251.501.75-2020
Plot the graph f(x)
The answer [src] 
-81/4
−814- \frac{81}{4} 
=
= 
-81/4
−814- \frac{81}{4} 
-81/4
Numerical answer [src] 
-20.25
-20.25

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

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