a. Explanation Given information: The velocity function is given as v ( t ) = − 0.22 t 2 + 8.8 t over the time interval [ 0 , 40 ] in seconds with n = 4 . Calculation: When calculating the midpoint sum, the mid value of each subinterval is used to obtain the height of the rectangles. For equal four rectangles, the width should be 10 and the mid points should be 5 , 15 , 25 and 35 respectively. A table is constructed for further calculations for the height of the rectangles. Midpoint Calculation − 0.22 t 2 + 8.8 t Height 0.5 − 0.22 ( 5 ) 2 + 8.8 ( 5 ) 38.5 1.5 − 0.22 ( 15 ) 2 + 8 b. To determine To find: The approximate distance travelled as the trapezoids.

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 4.2, Problem 46A

To determine

To find:The approximate the distance travelled as the midpoint sum.

To determine

To find:The approximate distance travelled as the trapezoids.

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Chapter 4.2, Problem 45A

Chapter 4.2, Problem 47A

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Chapter 4 Solutions

Calculus

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The approximate the distance travelled as the midpoint sum.

Solution Summary: The author calculates the distance travelled as the midpoint sum. The car has been driven approximately 2420 feet within this 40 second.