Find a Bound on the Error in Approximating the Given

question 121

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 seven 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 seven decimal places.

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Definitions:

Tube-Within-a-Tube

A design characteristic of the body plans of many animals, where the outer tube represents the body wall, and the inner tube represents the alimentary canal or gut.

Flukes

Parasitic flatworms that infect the liver, lungs, and other organs of their hosts, with life cycles involving one or more intermediate hosts.

Oral Sucker

A muscular structure found in some animals, such as parasitic worms, used for attachment to or ingestion of food from hosts or surfaces.

Alimentary Canal

A series of hollow organs joined in a long, twisting tube from the mouth to the anus, through which food is digested and nutrients are absorbed.