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Chapter 13: Q 6. (page 1014)

Which of the iterated integrals in Exercises below could correctly

be used to evaluate the double integral:

鈭�41鈭�62f(x,y)dydx

Short Answer

Expert verified

The iterated integral giving correct value of鈭�Rf(x,y)dA is鈭�14鈭�26f(x,y)dydx

Step by step solution

01

Given Information

Rectangular region is bounded by linesx=1,x=4,y=2andy=6

02

Simplification

In iterated integral 鈭�41鈭�62f(x,y)dydx, inner integral is w.r.t yand limits are of yof inner integral.

This is true for xalso, the limits are reversed.

Hence, iterated integral will give incorrect value of 鈭�Rf(x,y)dA.

The region is bounded by y=2below, y=6above, x=1to left and x=4to right.

Hence, iterated integral that will give correct value of integral鈭�Rf(x,y)dA is鈭�14鈭�26f(x,y)dydx

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