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

question 112

Multiple Choice

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 8 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.
$\int _ { 4 } ^ { 5 } \sqrt { 4 + t ^ { 5 } } d t$

• A) The Trapezoidal rule gives \(43.377044\) and Simpson's rule gives \(45.513198\).
• B) The Trapezoidal rule gives \(43.345903\) and Simpson's rule gives \(43.335523\).
• C) The Trapezoidal rule gives 43.377044 and Simpson's rule gives 43.335523.
• D) The Trapezoidal rule gives \(43.345903\) and Simpson's rule gives \(45.513198\).
• E) The Trapezoidal rule gives \(- 43.345903\) and Simpson's rule gives \(- 43.335523\).

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