Use the Midpoint Rule with $n = 4$ to approximate $\pi$ where $\pi = \int _ { 0 } ^ { 1 } \frac { 4 } { 1 + x ^ { 2 } } d x$ . Then use a graphing utility to evaluate the definite integral. Compare your results.
A)a. Midpoint Rule: $\approx 0.146801$ b. Graphing utility: $\approx 3.141593$
B)a. Midpoint Rule: $\approx 3.146801$ b. Graphing utility: $\approx 0.141593$
C)a. Midpoint Rule: $\approx 1.146801$ b. Graphing utility: $\approx 3.141593$
D)a. Midpoint Rule: $\approx 3.146801$ b. Graphing utility: $\approx 3.141593$
E)a. Midpoint Rule: $\approx 3.146801$ b. Graphing utility: $\approx 1.141593$

Question

Quizplus · Accepted Answer

The Midpoint Rule approximation for $\pi$ using $n = 4$ should be close to the actual value of $\pi$, which is approximately 3.141593. The correct option is the one where both the Midpoint Rule approximation and the graphing utility's evaluation are close to this value.

Use the Midpoint Rule With n=4n = 4n=4 To Approximate π\piπ Where π=∫0141+x2dx\pi = \int _ { 0 } ^ { 1 } \frac { 4 } { 1 + x ^ { 2 } } d xπ=∫01​1+x24​dx

Use the Midpoint Rule With $n = 4$ To Approximate $\pi$ Where $\pi = \int _ { 0 } ^ { 1 } \frac { 4 } { 1 + x ^ { 2 } } d x$