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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Using the Trapezoidal Rule and Simpson’s Rule In Exercises 11-20, approximate the value of the definite integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of n. Round your answers to three decimal places. See Examples 1 and 2.

0 1 1 1 + x 2 d x , n = 4

(a)

To determine

To calculate: The value of the integral 0111+x2dx,n=4 by using the Trapezoidal Rule and to approximate the value of the definite integral for the indicated value of n.

Explanation

Given Information:

The provided definite integral is 0111+x2dx.

Formula used:

Trapezoidal Rule:

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

abf(x)dx(ba2n)[f(x0)+2f(x0)+...+2f(xn1)+f(xn)]

Calculation:

Consider the provided information,

Consider the definite integral 0111+x2dx.

When n=4, the width of each subinterval is

Δx=104=14

And the end points of subintervals are given below,

x0=0,x1=14,x2=14+14=12,<

(b)

To determine

To calculate: The value of the integral 0111+x2dx,n=4 by using the Simpson’s Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to four decimal places.

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