Using Simpson's Rule with n = 4, the approximated value of $\int _ { \pi } ^ { 2 \pi } \frac { \sin x } { x } d x,$ to three decimal places, is

A) $- 0,125$
B) $- 0.248$
C) $- 0.635$
D) $- 0.434$
E) $- 0.737$

Question

Using Simpson's Rule with n = 4, the approximated value of $\int _ { \pi } ^ { 2 \pi } \frac { \sin x } { x } d x,$ to three decimal places, is

A) $- 0,125$
B) $- 0.248$
C) $- 0.635$
D) $- 0.434$
E) $- 0.737$

Quizplus · Accepted Answer

Simpson's Rule is used to approximate the integral by dividing the interval into an even number of subintervals (n=4 here). The function values at these points are used in the formula. Calculating using Simpson's Rule for this integral gives approximately -0.434.

Using Simpson's Rule with N = 4, the Approximated Value ∫π2πsin⁡xxdx,\int _ { \pi } ^ { 2 \pi } \frac { \sin x } { x } d x,∫π2π​xsinx​dx,

Using Simpson's Rule with N = 4, the Approximated Value $\int _ { \pi } ^ { 2 \pi } \frac { \sin x } { x } d x,$