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Solving integrals/ x^2-16

Integral of x^2-16 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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4
∫45(x2−16) dx\int\limits_{4}^{5} \left(x^{2} - 16\right)\, dx 
Integral(x^2 - 16, (x, 4, 5))
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:

      ∫x2 dx=x33\int x^{2}\, dx = \frac{x^{3}}{3}

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

      ∫(−16) dx=−16x\int \left(-16\right)\, dx = - 16 x

    The result is: x33−16x\frac{x^{3}}{3} - 16 x

  2. Now simplify:

    x(x2−48)3\frac{x \left(x^{2} - 48\right)}{3}

  3. Add the constant of integration:

    x(x2−48)3+constant\frac{x \left(x^{2} - 48\right)}{3}+ \mathrm{constant}

The answer is:

x(x2−48)3+constant\frac{x \left(x^{2} - 48\right)}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                            
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 | \x  - 16/ dx = C - 16*x + --
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∫(x2−16) dx=C+x33−16x\int \left(x^{2} - 16\right)\, dx = C + \frac{x^{3}}{3} - 16 x
Simplify
The graph
4.005.004.104.204.304.404.504.604.704.804.90-5050
Plot the graph f(x)
The answer [src] 
13/3
133\frac{13}{3} 
=
= 
13/3
133\frac{13}{3} 
13/3
Numerical answer [src] 
4.33333333333333
4.33333333333333

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

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