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.
Definitions:
Social Change
Alterations in the social structure and cultural values of a society over time.
Industrial Activity
Economic activities related to the production of goods and services in sectors such as manufacturing, mining, and construction.
Economic Change
Alterations in the structure, performance, or operations of an economy, often marked by growth or decline.
Manufacturing
The process of converting raw materials into finished goods through the use of tools, machinery, and labor.
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