   Chapter 15.1, Problem 5E

Chapter
Section
Textbook Problem

Let V be the volume of the solid that lies under the graph of f ( x , y ) = 52 − x 2 − y 2 and above the rectangle given by 2 ≤ x ≤ 4, 2 ≤ y ≤ 6. Use the lines x = 3 and y = 4 to divide R into subrectangles. Let L and U be the Riemann sums computed using lower left corners and upper right corners, respectively. Without calculating the numbers V, L, and U, arrange them in increasing order and explain your reasoning.

To determine

To arrange: The given three numbers V,L&U in increasing order with justification.

Explanation

Given:

The function, f(x,y)=52x2y2,R={(x,y)|2x4,2y6}

The volume of the solid is denoted by V .

The upper Riemann sum computed using upper right corners is denoted by U .

The lower Riemann sum computed using lower left corners is denoted by L .

Reason:

Express the given function as, f(x,y)=52(x2+y2)

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