Chapter 13: Q 12. (page 1014)

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

Short Answer

Expert verified

$\int_{0}^{2} \int_{0}^{- y + 2} f (x, y) d x d y$ will give the correct value of the given integral.

Step by step solution

Given Information

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

Consideration

Consider iterated integral

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

Region is triangular and can be of any type.

For type II region, inner integral is solved wrt $x$ .

This is not true for iterated integral $\int_{2}^{0} \int_{- y + 2}^{0} f (x, y) d x d y$

Simplification

Keeping the order of integral same, limits of both inner and outer integral should be reversed.

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

Therefore, iterated integral $\int_{0}^{2} \int_{0}^{- y + 2} f (x, y) d x d y$ will give the 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 $\iint_{0} f (x, y) d A$
$\int_{2}^{0} \int_{- y + 2}^{0} f (x, y) d x d y$

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 ∬0f(x,y)dA∫20∫-y+20f(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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Which of the iterated integrals in Exercises 9–12 could correctly be used to evaluate the double integral $\iint_{0} f (x, y) d A$
$\int_{2}^{0} \int_{- y + 2}^{0} f (x, y) d x d y$