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 \(0.7380\).

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Definitions:

Psychoanalysis

A therapeutic approach and theory of psychology developed by Sigmund Freud, which emphasizes exploring unconscious motives and conflicts.

Free Association

A psychoanalytic technique in which a patient says whatever comes to mind without censorship, used to explore subconscious thoughts and feelings.

Psychoanalysis

A method of psychology founded by Sigmund Freud, focusing on exploring unconscious motives and conflicts.

Rational-Emotive Therapy

A form of cognitive-behavioral therapy founded by Albert Ellis that helps individuals identify and challenge irrational beliefs, encouraging more realistic and self-helping thoughts.