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

Multiple Choice

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: $\approx 1.141593$