Chapter 13: Q 6. (page 1014)

Which of the iterated integrals in Exercises below could correctly
be used to evaluate the double integral:
$\int_{4}^{1} \int_{6}^{2} f (x, y) d y d x$

Short Answer

Expert verified

The iterated integral giving correct value of $\iint_{R} f (x, y) d A$ is $\int_{1}^{4} \int_{2}^{6} f (x, y) d y d x$

Step by step solution

Given Information

Rectangular region is bounded by lines $x = 1, x = 4, y = 2 and y = 6$

Simplification

In iterated integral $\int_{4}^{1} \int_{6}^{2} f (x, y) d y d x$ , inner integral is w.r.t $y$ and limits are of $y$ of inner integral.

This is true for $x$ also, the limits are reversed.

Hence, iterated integral will give incorrect value of $\iint_{R} f (x, y) d A$ .

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

Hence, iterated integral that will give correct value of integral $\iint_{R} f (x, y) d A$ is $\int_{1}^{4} \int_{2}^{6} f (x, y) d y d x$

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Which of the iterated integrals in Exercises below could correctly
be used to evaluate the double integral:
$\int_{4}^{1} \int_{6}^{2} f (x, y) d y d x$

Short Answer

Step by step solution

Given Information

Simplification

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Which of the iterated integrals in Exercises below could correctlybe used to evaluate the double integral:∫41∫62f(x,y)dydx

Short Answer

Step by step solution

Given Information

Simplification

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Which of the iterated integrals in Exercises below could correctly
be used to evaluate the double integral:
$\int_{4}^{1} \int_{6}^{2} f (x, y) d y d x$