Prove That $\frac { - x ^ { 3 } } { 3 } \cos x$

question 9

Essay

Prove that $\frac { - x ^ { 3 } } { 3 } \cos x$ is not an antiderivative of $x ^ { 2 } \sin x$ .

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Definitions:

End Result

The final outcome or conclusion of a process or a series of actions.

Rule Utilitarianism

A form of utilitarianism that says an action is right as it conforms to a rule that leads to the greatest good, or that "the rightness or wrongness of a particular action is a function of the correctness of the rule of which it is an instance."

Act Utilitarianism

A moral theory that suggests an action is right if it leads to the most happiness for the greatest number of people, evaluating each act separately.

Overall Utility

Refers to the total benefit or satisfaction gained from consuming a good or service, taking into account all aspects of its use.