Answer:
To evaluate the definite integral
[tex]\int_{2}^{2} 2x (x^{2} + 4)^{2} \, dx, [/tex]
we can observe that the limits of integration are the same, which means the integral evaluates to zero. This is a fundamental property of definite integrals.
Formally, for any function ( f(x) ):
[tex] \int_{a}^{a} f(x) \, dx = 0[/tex]
Therefore, the result is:
[tex]\int_{2}^{2} 2x (x^{2} + 4)^{2} \, dx = 0[/tex]
The result of the integral is:
[tex] \boxed{0} [/tex]
