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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Approximation The table shows values of a function f over a square region R. Divide the region into 16 equal squares and select ( x i , y i ) to be the point in the ith square closest to the origin. Approximate the value of the integral below. Compare this approximation with that obtained by using the point in the ith square farthest from the origin.

0 4 0 4 f ( x , y ) d y d x

x \y 0 1 2 3 4
0 32 31 28 23 16
1 31 30 27 22 15
2 28 27 24 19 12
3 23 22 19 14 7
4 16 15 12 7 0

To determine

To calculate: What the approximate value of integral 0404f(x,y)dydx will be and then, comparing the calculated value with that obtained by using the point in ith square farthest from the origin.

Explanation

Given:

The values of a function x over a square region R,

x\y012340323128231613130272215228272419123232219147416151270

Calculation:

In order to calculate the integral 0404f(x,y)dydx, 16 values of (xi,yj) are chosen that are closest to the origin which means values of (x0,y0),(x0,y1),(x0,y2)(x3,y3)

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Chapter 14 Solutions

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