Apply the Trapezoidal Rule and Simpson's Rule to Approximate the Value

question 157

Multiple Choice

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 4 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.
$\int _ { 4 } ^ { 7 } \frac { 1 } { \sqrt { t } \sqrt { 9 - t } } d t$

• A) The Trapezoidal rule gives \(0.7100\) and Simpson's rule gives \(0.7005\).
• B) The Trapezoidal rule gives \(- 0.7028\) and Simpson's rule gives \(- 0.7005\).
• C) The Trapezoidal rule gives \(0.7100\) and Simpson's rule gives \(0.7380\).
• D) The Trapezoidal rule gives \(0.7028\) and Simpson's rule gives \(0.7005\).
• E) The Trapezoidal rule gives \(0.7028\) and Simpson's rule gives \(0.7380\).

Understand and apply strategies for preventing and correcting errors in math tests.

Understand the benefits of collaborative study for exam preparation.

Recognize the importance of perspective and constructive outlook towards evaluations and feedback.

Understand the need to prepare for a variety of question types on tests.

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Definitions:

Direct Materials

Raw materials that can be directly attributed to the production of finished goods.

Relevant Range

The spectrum of operations within which the behaviors of variable and fixed costs are considered accurate.

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Definition: Decisions made by management related to the day-to-day operations of a company, including costs, production, and pricing strategies.

Strategic Level

A high-level perspective in organizational planning that focuses on long-term goals and overall direction of an organization.