Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximatingrectanglesA = lim Rn = lim [f(x1)Ax + f(xæ2)Ar+.+f(xn)Az]n00n00(a) Use the above definition to determine which of the following expressions represents the area under the graph of f(x) = x³ from x = 0 to x = 2.6425TH00 TL i=1A. lim1В. limn+00 n664C. lim64D. limn-00 n6i=1(b) Evaluate the limit that is the correct answer to part (a). You may find the following formula helpful:15 + 25 + 35+.+n³ =25n2(n + 1)²(2n² + 2n – 1)12Value of limit =

Limit definition of the definite Integral

Answered: Definition: The AREA A of the region S…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.1: Inverse Functions

Problem 62E

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Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles.
Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles PS: For (a) it is only choosing one of the right selection to determine.
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