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(a) Use the definition given below with right endpoints to express the area under the curve y = x³ from 0 to 1 as a limit. The area A of the region S that is bounded above by the graph of a continuous function y = f(x), below by the x-axis, and on the sides by the lines x = a and x = b is the limit of the sum lim A lim R lim [f(x₂)Ax + f(x₂)Ax + + f(x)Ax] lim i-1 i-1 13+23+33+. ·+n³= f(x,)AX (b) Use the following formula for the sum f cubes of the first n integers to evaluate the limit in part (a). - [ n(n+1)]² the areas of approximating rectangles.

(a) Use the definition given below with right endpoints to express the area under the curve y = x³ from 0 to 1 as a limit. The area A of the region S that is bounded above by the graph of a continuous function y = f(x), below by the x-axis, and on the sides by the lines x = a and x = b is the limit of the sum lim A lim R lim [f(x₂)Ax + f(x₂)Ax + + f(x)Ax] lim i-1 i-1 13+23+33+. ·+n³= f(x,)AX (b) Use the following formula for the sum f cubes of the first n integers to evaluate the limit in part (a). - [ n(n+1)]² the areas of approximating rectangles.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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(a) Use the definition given below with right endpoints to express the area under the curve y = x³ from 0 to 1 as a limit. The area A of the region S that is bounded above by the graph of a continuous function y = lim n→∞ A = n i = 1 lim Rn n→∞ = lim_[f(x₁)Ax + f(x₂)Ax + n→∞ +n³. = + f(x)Ax] = lim n→∞ (b) Use the following formula for the sum of cubes of the first n integers to evaluate the limit in part (a). 13 + 23 +33 + n(n + 1) 2 12 f(x;)Ax f(x), below by the x-axis, and on the sides by the lines x = a and x = b is the limit of the sum of the areas of approximating rectangles.
Transcribed Image Text:(a) Use the definition given below with right endpoints to express the area under the curve y = x³ from 0 to 1 as a limit. The area A of the region S that is bounded above by the graph of a continuous function y = lim n→∞ A = n i = 1 lim Rn n→∞ = lim_[f(x₁)Ax + f(x₂)Ax + n→∞ +n³. = + f(x)Ax] = lim n→∞ (b) Use the following formula for the sum of cubes of the first n integers to evaluate the limit in part (a). 13 + 23 +33 + n(n + 1) 2 12 f(x;)Ax f(x), below by the x-axis, and on the sides by the lines x = a and x = b is the limit of the sum of the areas of approximating rectangles.
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