   Chapter 7.7, Problem 8E

Chapter
Section
Textbook Problem

# Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule to approximate the given integral with the specified value of n. (Round your answers to six decimal places.) ∫ 0 2 1 1 + x 6   d x ,      n = 8

To determine

(a)

To find: Approximate integral using the trapezoidal rule

Explanation

Given:

f(x)=11+x6,a=0,b=2,n=8

Δx=ban=28=0.25

Formula used:

Tn=Δx2[f(x0)+2f(x1)+2f(x2)++2f(xn1)+f(xn)]

T8=Δx2[f(0)+2f(0

To determine

(b)

To find: Approximate integral using the Midpoint rule

To determine

(c)

To find: Approximated integral using Simpson’s rule

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