Find a Bound on the Error in Approximating the Given

question 161

Essay

Find a bound on the error in approximating the given definite integral using the trapezoidal rule with n intervals. If necessary, round the answer to three decimal places.
Find a bound on the error in approximating the given definite integral using the Simpson's rule with n intervals. If necessary, round the answer to five decimal places.

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Definitions:

Industrial Capitalism

An economic system characterized by private or corporate ownership of capital goods, production for profit, and the predominance of industrial manufacturing and finance.

Advances in Technology

Refers to the progressive developments and innovations in various fields such as science, engineering, and information technology that enhance capabilities and efficiency.

European Imperialism

The policy of extending a country's power and influence through colonization, use of military force, or other means, particularly by European nations from the 16th to the 20th century.

Positivism

A philosophical approach advocating for the reliance on empirical evidence and scientific methods to acquire knowledge, minimizing metaphysical speculation.