Question: Suppose (x, y) is continuous and nonnegative over a region R in the plane with a defined area A(R). If R (x, y) dA

Suppose ƒ(x, y) is continuous and nonnegative over a region R in the plane with a defined area A(R). If ∫∫_R ƒ(x, y) dA = 0, prove that ƒ(x, y) = 0 at every point (x, y) ε R.

Step by Step Solution

★★★★★

3.39 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Suppose x y is continuous and nonnegative over a region R in t... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

The random vector (X, Y) is said to be uniformly distributed over a region R in the plane if, for some constant c, its joint density is (a) Show that 1/c = area of region R. Suppose that (X, Y) is...

Suppose (x, y) is continuous over a region R in the plane and that the area A(R) of the region is defined. If there are constants m and M such that m (x, y) M for all (x, y) R, prove that mA(R)

Suppose that a a) If f is continuous and nonnegative on [a, b] and g : [a, b] [a, b] is differentiable and increasing on [a, b], then is increasing on [a, b]. b) If f and g are differentiable on [a,...

Calculus 3 Sections 15.1 - 15.2 Reading Assignment: Double Integrals Question 2: Explain each step of the procedure for finding the limits of integration when integrating in the order dx dy. Hint 1:...

3-4-2 If writing process is bothering you, it's ok to write only correct answer in each question. 1. Let f (x) = v2 - C. Find the average value of f (x) on the interval [-2, 2]. Preview will appear...

Write an iterated integral of a continuous function f over the region R shown in the figure. + 15 10- y= 2 x 5 - R X . . Write an iterated integral of a continuous function f. f(x,y) dx dy\fEvaluate...

The average value or mean value of a continuous function f (x, y) over a region R in the xy-plane is defined as fave A (R) where A (R) is the area of the region R. Use this definition in this...

The likelihood that a person with a contagious disease will infect others in a social situation may be assumed to be a function f(s) of the distance s between individuals. Suppose contagious...

Question 6. [10 marks] Let a denote a positive constant. It is known that the graph of has a loop which bounds a region R in the ry-plane and the area of R is a?. Suppose (x -4) dA = 0. Determine the...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Find the extreme points of P. Let P = {x E R : Ax 0}, where 1 2 1 -3 3 A and b 1 4 -2

Under what circumstances do you believe MBO would be most useful? Discuss.

Which one of these bonds is the most interest - rate sensitive ? Select one or more: a . 1 0 - year zero coupon bond b . 1 0 - year, 6 percent, annual coupon bond c . 5 - year zero coupon bond d . 5...

15.17 The paper referenced in the previous exercise also gave the following underscoring pattern for men: Treatment: 2 1 3 4 Mean number of pretzels consumed: 6.61 5.96 3.38 2.70 a. Write a few...

In Exercises 3540, find the tangential and normal components of acceleration at the given time t for the space curve (r)t. r(t) = ti + Aj + 2/2k, -k. t = 1

Sketch the space curve represented by the vector-valued function and give the orientation of the curve. r(t) = t 2 i + 2tj + 3/2 tk

In Exercises 3540, find the tangential and normal components of acceleration at the given time t for the space curve (r)t. r(t) = ti + 2tj - 3tk, t = 1

The traditional income statement produced by the financial accounting system and required for external reporting: a. organizes cost by behavior ( variable vs. fixed costs) rather than by function...

Incorrect Question 18 0/1 pts Which of the following is NOT a source of revenue growth? Increased brand recognition Acquisitions Increased market capitalization New product offerings See Chapter 16

Exchange Corp. is a company that acts as a facilitator in tax-favored real estate swaps. Such swaps, know as 1031 exchanges, permit participants to avoid some or all of the capital gains taxes that...