   Chapter 7.7, Problem 20E

Chapter
Section
Textbook Problem

# (a) Find the approximations T 10 and M 10 for ∫ 1 2 e 1 / x   d x .(b) Estimate the errors in the approximations of part (a).(c) How large do we have to choose n so that the approximations T n and M n to the integral in part (a) are accurate to within 0.0001?

To determine

(a)

To find: Integral approximate using Trapezoid rule and midpoint rule

Explanation

Formula used:

Tn=Δx2[f(0)+2i=1n1f(xi)+f(x)]

Mn=Δxi=1nf(x¯i)

Where x¯is are midpoint of subintervals

Given:I=12e1/xdx,f(x)=e1/xa=1,b=2,n=10

Δx=ban=110=0.1

For T10

T10=Δx2[f(1)+2f(1.1)+2f(1.2)+2f(1.3)+2f(1.4)+2f(1.5)+2f(1.6)+2f(1

To determine

(b) To find: Error estimates in the approximations

To determine

(c) To find:n such that

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