The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim Rn = lim [f(x,)Ax + f(x2)Ax + . . . + f(x,)Ax] n- co n - co Use this definition to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. f(x) = In(x) 6 < xs 11 n A = lim n - c0 i = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.6: Permutations
Problem 47E
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The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles.
A = lim R, = lim [f(x,)Ax + f(x,)Ax + . .. + f(x,)Ax]
n - co
n - co
Use this definition to find an expression for the area under the graph of f as a limit. Do not evaluate the limit.
In(x)
f(x)
6 < x < 11
A = lim
n - co
1 = 1
Transcribed Image Text:The area A of the region S that lies under the graph of the continuous function is the limit of the sum of the areas of approximating rectangles. A = lim R, = lim [f(x,)Ax + f(x,)Ax + . .. + f(x,)Ax] n - co n - co Use this definition to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. In(x) f(x) 6 < x < 11 A = lim n - co 1 = 1
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