Chapter 13: Q 9. (page 1014)

Which of the iterated integrals in Exercises 9–12 could correctly be used to evaluate the double integral $\iint_{Ω} f (x, y) d A$
$\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$

Short Answer

Expert verified

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

Step by step solution

Given Information

Rectangular region is bounded below $x$ axis, left by $y$ axis along the line $y = - x + 2$

Simplification

Consider an iterated integral $\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$

The region is triangular region, can be of any type.

For type I region, inner integral is wrt $y$

In $\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$ , inner integral is wrt $y$

It will give correct value of $\iint_{Ω} f (x, y) d A$

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Which of the iterated integrals in Exercises 9–12 could correctly be used to evaluate the double integral $\iint_{Ω} f (x, y) d A$
$\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$

Short Answer

Step by step solution

Given Information

Simplification

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Which of the iterated integrals in Exercises 9–12 could correctly be used to evaluate the double integral ∬Ωf(x,y)dA∫02∫0-x+2f(x,y)dydx

Short Answer

Step by step solution

Given Information

Simplification

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Most popular questions from this chapter

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Which of the iterated integrals in Exercises 9–12 could correctly be used to evaluate the double integral $\iint_{Ω} f (x, y) d A$
$\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$