   Chapter 7.R, Problem 66E

Chapter
Section
Textbook Problem

# Use Simpson’s Rule with n = 60 to estimate the area under the curve y = e x / x from x = 1 to x = 4 .

To determine

To estimate:

The area under the curve using Simpson’s Rule with n = 6.

Explanation

Given:

y=ex from x=1 to x=4

Formulae used:

The Simpson’s Rule.

Consider y=ex and n=6

Hence, to use the Simpson’s rule

Interval width:

Δx=ban=416=0.5

So the point are 1, 1.5, 2, 2.5, 3, 3.5, 4.

As the graph of the curve y=ex is totally above the x-axis for the interval.

Thus, the Simpson’s rule formula with n+1=7 terms

S6=14exxdxΔx3[f(x0)+4f(

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