   Chapter 4, Problem 25RE

Chapter
Section
Textbook Problem

Finding Upper and Lower Sums for a Region In Exercises 25 and 26, use upper and lower sums to approximate the area of the region using the given number of subintervals(of equal width.) y = 10 x 2 + 1 To determine

To calculate: The approximate area of the shaded region by using both the upper and lower sums for the curve y=10x2+1.

Explanation

Given:

The curve y=10x2+1 and the shaded region:

Calculation:

The step-size has been provided as Δx=0.5. So for the upper sum, the values of ci would be the 4 right-most grid points where the interval [0,2] is divided into 4 parts using the 5 points 0, 0.5, 1, 1.5, 2.

This gives the upper sum as:

S=i=14y(ci)Δxi=y(0.5)(0.5)+y(1)(0.5)+y(1.5)(0.5)+y(2)(0.5)=(100.52+1)(0.5)+(1012+1)(0.5)+(101.52+1)(0.5)+(1022+1)(0

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