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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5, Problem 110RE
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Using the Midpoint Rule In Exercises 105-110, use the Midpoint Rule with n = 4 to approximate the area of the region bounded by the graph of f and the x-axis over the interval. Sketch the region.

Function Interval

f ( x ) = 3 x x 3 + 2      [0,4]

To determine

To calculate: The area of the region bounded by the graph of the function f(x)=3xx3+2 where the intervals are [0,4] use midpoint rule with n as 4 and sketch the region.

Explanation

Given Information:

The provided function is f(x)=3xx3+2 and the intervals is intervals are [0,4]

Formula used:

Steps to solve a definite integral ∫abf(x)dx with the help of midpoint rule.

Step 1: For a given interval [a,b] divide it into n subintervals with having width of,

Δx=b−an

Step 2: Evaluate the midpoint for the given subinterval. Midpoints={x1,x2,x3,…xn}

Step 3: Find the value of f at each midpoint and make the sum as shown below:

∫abf(x)dx≈b−an[f(x1)+f(x2)+f(x3)+⋯+f(xn)]

Calculation:

Consider the function,

f(x)=3xx3+2

The intervals are [0,4] with n=4.

Now divide the provided interval into 4 subparts as shown below,

Δx=4−04=1

Therefore the 4 subintervals are,

[0,1],[1,2],[2,3],[3,4]

Now find the mid points of these intervals because each subinterval has a width of 1. Therefore, the mid points of these interval are shown below:

12,32,52 and 72

Here the mid points 12,32,52 and 72 lies in the middle of [0,1],[1,2],[2,3],[3,4] intervals respectively

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Research Methods for the Behavioral Sciences (MindTap Course List)

Find the values of x and y. x+5i=y-yi

College Algebra (MindTap Course List)

The National Association of Realtors reported the median home price in the United States and the increase in me...

Statistics for Business & Economics, Revised (MindTap Course List)

The article Cops Get Screened for Digital Dirt (USA TODAY, November 12, 2010) summarizes a report of law enforc...

Introduction To Statistics And Data Analysis

Determine the unknown value for each of the following exercises. Round the answers to 3 decimal places. Arc len...

Mathematics For Machine Technology

Suppose a researcher conducts a two-factor study comparing two treatments (I and II) for college graduates vers...

Research Methods for the Behavioral Sciences (MindTap Course List)

Given are data for two variables, x and y. xi 6 11 15 18 20 yi 6 8 12 20 30 a. Develop an estimated regression ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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