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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

The environmental effects of a chemical spill in the Clarion River can be estimated from the river's flow volume. To measure this flow volume, it is necessary to find the cross-sectional area of the river at a point downriver from the spill. The distance across the river is 240 feet, and the table gives depth measurements, D(x), in feet, of the river at various distances x from one bank of the river. Use these measurements with Simpsons Rule to estimate the cross-sectional area.

X 0 40 80 120 160 200 240
D(x) 0 22 35 48 32 24 0

To determine

To calculate: The cross-sectional area by Simpson’s rule if the distance across the river is 240 feet and the depth measurements D(x) in feet at various distances x from one bank of the river is provided in the table.

x04080120160200240D(x)022354832240

Explanation

Given Information:

The distance across the river is 240 feet and the depth measurements D(x) in feet at various distances x from one bank of the river is provided in the table.

x04080120160200240D(x)022354832240

Formula used:

Simpson’s Rule for a continuous function f(x) on the interval [a,b] which is divided into an even number n of equal subdivisions then,

abf(x)dxh3[f(x0)+4f(x1)+2f(x2)+4f(x3)++2f(xn2)+4f(xn1)+f(xn)]

Where, h=ban.

Calculation:

Consider the values of x,

x0x1x2x3x4x5x604080120160200240

Also, the values of function D(x)<

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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