a . Explanation Given: The given graphs are Area between the graph of f ( x ) = 4 − x 2 and the x-axis on [ 0 , 2 ] . Calculation: Area of the four rectangle graph. Width of each rectangle = 1 2 The height of the rectangles are given in the graph. Area ( A ) = f ( 0 ) ⋅ 1 2 + f ( 1 2 ) ⋅ 1 2 + f ( 1 ) ⋅ 1 2 + f ( 3 2 ) ⋅ 1 2 = 1 2 [ f ( 0 ) + f ( 1 2 ) + f ( 1 ) + f ( 3 2 ) ] = 1 2 [ ( 4 − 0 ) + ( 4 − 1 4 ) + ( 4 − 1 ) + ( 4 − 9 4 ) ] = 1 2 [ 4 + 15 4 + 3 + 7 4 ] = 1 2 [ 16 + 15 + 12 + 7 4 ] = 50 8 = 6.25 Area of the eight rectangle graph. Width of each rectangle = 1 4 The height of the rectangles are given in the graph b . To determine Explain, if the same process did by more and more rectangles.

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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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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Question

Chapter 1.1, Problem 15C

To determine

Find the area of the rectangles using given graphs.

To determine

Explain, if the same process did by more and more rectangles.

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Chapter 1.1, Problem 14C

Chapter 1.1, Problem 16C

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Chapter 1 Solutions

Calculus

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Find the area of the rectangles using given graphs.

Solution Summary: The author calculates the area of the rectangles using given graphs.

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Find the area of the rectangles using given graphs.

Explain, if the same process did by more and more rectangles.

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Chapter 1 Solutions