   Chapter 13, Problem 15T ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# use the trapezoidal Rule to approximate ∫ 1 3 ( x ln x ) d x With n = 4 subintervals

To determine

To calculate: The value of 13(xlnx)dx for n=4 subintervals by the use of the Trapezoidal Rule.

Explanation

Given Information:

The provided integral is 13(xlnx)dx with n=4 subintervals.

Formula used:

The Trapezoidal Rule for function f on the interval [a,b] is,

abf(x)dxh2[f(x0)+2f(x1)++2f(xn1)+f(xn)]

Where, h=ban and n is the number of equal subdivisions of [a,b].

Calculation:

Consider the integral,

13(xlnx)dx

The number of subdivisions is n=4 and the value of a and b are 1 and 3 respectively.

The function is,

f(x)=xlnx

By Trapezoidal Rule,

abf(x)dx=h2[f(x0)+2f(x1)+.....+2f(xn1)+f(xn)]

The value of h is,

h=ban=314=0

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