Chapter 13: Q 10. (page 1014)

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

Short Answer

Expert verified

The iterated integral that will give correct value of integral is $\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$

Step by step solution

Given Information

It is given that region is bounded on left by $y$ axis and on left by $x$ axis.

Consideration

Consider iterated integral

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

Region is triangular and can be of any type.

The inner integral is solved wrt $y$ for type I.

Simplification

But in iterated integral $\int^{- x + 2} \int^{2} f (x, y) d x d y$ , inner integral is wrt $y$

Hence, it will give incorrect value of $\iint_{Ω} f (x, y) d A$

The limits will be interchanged and hence the correct integral is $\int_{0}^{2} \int_{0}^{- x + 2} f (x, y) d y d x$

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

Short Answer

Step by step solution

Given Information

Consideration

Simplification

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

Short Answer

Step by step solution

Given Information

Consideration

Simplification

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

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