   Chapter 4, Problem 29RE

Chapter
Section
Textbook Problem

Finding Area by the Limit Definition In Exercises 29-32, use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region. y = 8 − 2 x ,       [ 0 ,   3 ]

To determine

To calculate: Thearea of the region bounded by graph of function y=82x and the x axis by the Limit Definition

Explanation

Given:

y=82x in the interval [0,3]

Formula used:

S(n)=i=1nf(Mi)Δx

Calculation:

Partition the interval [0,3] in to n subinterval, each of which having fixed width

Δx=30n=3n

Therefore, the left end points of the interval

mi=0+(i1)(3n)=3(i1)n

And the right end points are

Mi=0+i(3n)=3in

By using the right end points the upper sum of the region is

S(n)=i=1nf(Mi)Δx=i=1nf(3in)(3n)=3ni=1n(86in)=3ni=1n818

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