Integral of (x+2)(x-2) dx

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$$\int\limits_{0}^{1} \left(x - 2\right) \left(x + 2\right)\, dx$$

Integral((x + 2)*(x - 2), (x, 0, 1))

Detail solution

Rewrite the integrand:

$\left(x - 2\right) \left(x + 2\right) = x^{2} - 4$
Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-4\right)\, dx = - 4 x$
The result is: $\frac{x^{3}}{3} - 4 x$
Now simplify:

$\frac{x \left(x^{2} - 12\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 12\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 12\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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 | (x + 2)*(x - 2) dx = C - 4*x + --
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$$\int \left(x - 2\right) \left(x + 2\right)\, dx = C + \frac{x^{3}}{3} - 4 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-11/3

$$- \frac{11}{3}$$

-11/3

$$- \frac{11}{3}$$

-11/3

Numerical answer [src]

-3.66666666666667

-3.66666666666667

The graph

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