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

question 46

Multiple Choice

Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the indicated value of n. Compare these results with the exact value of the definite integral. Round your answers to four decimal places. $\int _ { 0 } ^ { 1 } \left( \frac { x ^ { 2 } } { 2 } + 1 \right) d x , n = 4$

• A)a. Exact: \(\approx 1.9667\) b. Trapezoidal Rule: \(\approx 1.1719\) c. Simpson's Rule: \(\approx 1.1667\)
• B)a. Exact: \(\approx 1.1667\) b. Trapezoidal Rule: \(\approx 1.1719\) c. Simpson's Rule: \(\approx 1.9667\)
• C)a. Exact: \(\approx 1.1667\) b. Trapezoidal Rule: \(\approx 1.9719\) c. Simpson's Rule: \(\approx 1.1667\)
• D)a. Exact: \(\approx 2.1667\) b. Trapezoidal Rule: \(\approx 1.1719\) c. Simpson's Rule: \(\approx 1.1667\)
• E)a. Exact: \(\approx 1.1667\) b. Trapezoidal Rule: \(\approx 1.1719\) c. Simpson's Rule: \(\approx 1.1667\)

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