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Mathematical Applications for the ...

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

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BuyFindarrow_forward

Mathematical Applications for the ...

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

Use the Trapezoidal Rule with n = 5 to approximate

0 1 4 d x x 2 + 1

Round your answer to 3 decimal places.

To determine

To calculate: The approximate value of 014dxx2+1dx;n=5 using trapezoidal Rule.

Explanation

Given Information:

The provided integral is 014dxx2+1dx and the value of n is 5.

Formula used:

As per the Trapezoidal Rule:

If f is continuous on [a,b], then,

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++2f(xn2)+2f(xn1)+f(xn)]

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

Calculation:

Consider the provided integral,

014dxx2+1dx

And the value of n is 5.

In order to apply the rule, the value of h is as follows:

h=ban=105=15

Hence, the value of h is 15.

So, the interval [0,1] is divided into 5 subintervals as follows,

Put the values of the xi's in the equation

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)++2f(xn2

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Chapter 13 Solutions

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