   Chapter 14.1, Problem 79E

Chapter
Section
Textbook Problem

True or False? In Exercises 79 and 80, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ∫ a b ∫ c d d ( x , y ) d y   d x = ∫ c d ∫ a b f ( x , y ) d x   d y

To determine
Whether the statement “abcdf(x,y)dydx=cdabf(x,y)dxdy” is true or false.

Explanation

Consider a function,

f(x,y)=x2+y2

Consider the left-side of the provided statement,

abcdf(x,y)dydx=abcd(x2+y2)dydx=ab[x2y+y33]cddx=ab[x2(dc)+(dc)33]dx=[x33(dc)+(dc)33x]ab

Further,

[x33(dc)+(dc)33x]ab=[(ba)3(dc)+(dc)3(ba)3]

Therefore,

abcd(x2+y2)dydx=[(ba)3(dc)+(dc)3(ba)3]

Now, consider the right-side of the provided statement,

cdabf<

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