Chapter 13: Q 7. (page 1014)

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

Short Answer

Expert verified

The integral that will give 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 $x = 1, x = 4, y = 2 and y = 6$

Consideration

Consider integral

$\int_{1}^{4} \int_{2}^{6} f (x, y) d x d y$

The inner integral is wrt $x$ and limits of inner integral are of $y$ .

Same is applicable for $x$ .

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

Simplification

If region is considered of type I keeping limits same, order of integration should be same.

Inner integral is wrt $y$ .

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

Short Answer

Step by step solution

Given Information

Consideration

Simplification

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Which of the iterated integrals in Exercises below could correctlybe used to evaluate the double integral:∫14∫26f(x,y)dxdy

Short Answer

Step by step solution

Given Information

Consideration

Simplification

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Most popular questions from this chapter

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