Explanation Considering the definite integral: ∫ 2 5 ( 5 − x ) d x Sum of n rectangles is equal to on interval [a, b] is: ∑ k = 1 n f ( x k ) Δ x , here Δ x = b − a n = 5 − 2 n = 3 n and x k = a + k Δ x x k = 2 + k 3 n = 2 + 3 k n Now the sum is ; ∑ k = 1 n ( 5 − ( 2 − 3 k n ) ) ( 3 n ) = ( 3 n ) ∑ k = 1 n ( 3 − 3 k n ) <

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Chapter 4.3, Problem 18C

To determine

To proof : The sum of area of infinitely many rectangles which are infinitely thin is a finite number.

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Chapter 4.3, Problem 17C

Chapter 4.3, Problem 19C

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To proof : The sum of area of infinitely many rectangles which are infinitely thin is a finite number.

Solution Summary: The author explains that the sum of area of infinitely many rectangles is a finite number.

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To proof : The sum of area of infinitely many rectangles which are infinitely thin is a finite number.

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