   Chapter 6.3, Problem 20E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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 3 x 2 + x + x 2 d x , n = 6

(a)

To determine

To calculation: The value of the integral 03x2+x+x2dx,n=6 by using the Trapezoidal Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to four decimal places.

Explanation

Given Information:

The definite integral is 03x2+x+x2dx,n=6.

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:

Calculation by Trapezoidal Rule:

Consider the definite integral 03x2+x+x2dx,n=6.

When n=6, the width of each subinterval is

306=36=12

And the end points of subintervals are

x0=0x1=0.5x2=1x3=1.5

And,

x4=2x5=2.5x6=3

Thus, the graph of the function for interval,

(b)

To determine

To calculation: The value of the integral 03x2+x+x2dx,n=6 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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