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

question 58

Multiple Choice

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 20 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.
$\int _ { 1 } ^ { 2 } \left( 4 z ^ { 2 } + 7 \right) d z$

• A) The Trapezoidal rule gives \(16.3400\) and Simpson's rule gives 17,1518 .
• B) The Trapezoidal rule gives \(16.3400\) and Simpson's rule gives 16.3333.
• C) The Trapezoidal rule gives \(- 16.3350\) and Simpson's rule gives \(- 16.3333\).
• D) The Trapezoidal rule gives \(16.3350\) and Simpson's rule gives 16.3333.
• E) The Trapezoidal rule gives \(16.3350\) and Simpson's rule gives 17.1518.

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Definitions:

Sensory Information

Data received by the senses, which then may be interpreted by the brain.

Motor-Control Information

Information or feedback that is used to refine and adapt movements during motor task performance.

Parasympathetic Nervous System

Part of the autonomic nervous system responsible for conserving energy by slowing the heart rate and increasing intestinal and gland activity.

Autonomic Nervous System

The part of the nervous system responsible for control of bodily functions not consciously directed, such as breathing, the heartbeat, and digestive processes.