Find a Bound on the Error in Approximating the Given

question 249

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:

Igneous Feature

A geological formation that results from the solidification and crystallization of magma or lava, such as volcanoes or granite intrusions.

Batholith

A large mass of intrusive igneous rock, often granitic, that has solidified deep in the Earth's crust.

Decompression Melting

A geologic process where melting occurs due to a decrease in pressure as rock rises closer to the surface, without a change in temperature.

Subducting Plate

The tectonic plate that is being pushed downward into the mantle beneath another plate at a convergent boundary.