$\text { Use Simpson's Rule with } n = 14 \text { to approximate } \pi \text { using the equation }$ $\pi = \int _ { 0 } ^ { 1 } \frac { 4 } { 1 + x ^ { 2 } } d x$.
Round your answer to five decimal places.
A) $3.14159$
B) $3.13595$
C) $3.14723$
D) $3.14381$
E) $3.13937$

Question

$\text { Use Simpson's Rule with } n = 14 \text { to approximate } \pi \text { using the equation }$ $\pi = \int _ { 0 } ^ { 1 } \frac { 4 } { 1 + x ^ { 2 } } d x$. 
Round your answer to five decimal places.
A) $3.14159$
B) $3.13595$
C) $3.14723$
D) $3.14381$
E) $3.13937$

Quizplus · Accepted Answer

Simpson's Rule is a method for numerical integration. For the given integral, which represents the calculation of $\pi$, using Simpson's Rule with $n = 14$ steps provides an approximation very close to the actual value of $\pi$. The correct approximation to five decimal places is $3.14159$, which is the value of $\pi$ rounded to five decimal places. This demonstrates the effectiveness of Simpson's Rule for numerical integration, especially with a function that models a quarter circle, as in this case.

Use Simpson’s Rule with n=14 to approximate π using the equation \text { Use Simpson's Rule with } n = 14 \text { to approximate } \pi \text { using the equation } Use Simpson’s Rule with n=14 to approximate π using the equation

$\text { Use Simpson's Rule with } n = 14 \text { to approximate } \pi \text { using the equation }$