   Chapter 7.R, Problem 64E

Chapter
Section
Textbook Problem

# Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule with n = 10 to approximate the given integral. Round your answers to six decimal places. ∫ 1 4 x cos x   d x

To determine

( a)

To approximate:

The given integral using Trapezoidal Rule.

Explanation

Given:

14xcosxdx

Formulae used:

The integration by using Trapezoidal Rule.

Consider 14xcosxdx for n=10

Hence, use the integration by using Trapezoidal rule

Now according to the given expression, the value of the given expression 14xcosxdx is

Interval width

Δx=ban=4110=0.3

Trapezoidal rule has n+1=11 terms

T10=Δx2[f(1)+2f(1.3)+2f(1.6)+2f(1.9)+2f(2.2)+2f(2.5)+2f(2

To determine

(b)

To approximate:

The given integral using Midpoint Rule.

To determine

(c)

To approximate:

The given integral using by Simpson's Rule.

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