Chapter 13: Q 11. (page 1014)

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

Short Answer

Expert verified

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

Step by step solution

Given Information

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

Simplification

Consider iterated integral

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

Region is triangular and can be of either type

Inner integral is solved wrt $x$ for type II.

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

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

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-y+2f(x,y)dxdy

Short Answer

Step by step solution

Given Information

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