Q 11. Which of the iterated integrals ... [FREE SOLUTION]

Chapter 13: Q 11. (page 1014)

Which of the iterated integrals in Exercises 9鈥�12 could correctly be used to evaluate the double integral ${鈭�}_{惟} f (x, y) d A,$
${鈭�}_{0}^{2} {鈭�}_{0}^{- y + 2} f (x, y) d x d y$

Short Answer

Expert verified

The iterated integral ${鈭�}_{0}^{2} {鈭�}_{0}^{- y + 2} f (x, y) d x d y$ will give correct value of ${鈭�}_{惟} f (x, y) d A$

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

${鈭�}_{0}^{2} {鈭�}_{0}^{- y + 2} f (x, y) d x d y$

Region is triangular and can be of either type

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

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

Hence, it will give correct value of ${鈭�}_{惟} f (x, y) d A$

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91影视

Which of the iterated integrals in Exercises 9鈥�12 could correctly be used to evaluate the double integral ${鈭�}_{惟} f (x, y) d A,$
${鈭�}_{0}^{2} {鈭�}_{0}^{- y + 2} f (x, y) d x d y$

Short Answer

Step by step solution

Given Information

Simplification

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91影视

Which of the iterated integrals in Exercises 9鈥�12 could correctly be used to evaluate the double integral鈭�惟f(x,y)dA,鈭�02鈭�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

Recommended explanations on Math Textbooks

Geometry

Logic and Functions

Statistics

Decision Maths

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Which of the iterated integrals in Exercises 9鈥�12 could correctly be used to evaluate the double integral ${鈭�}_{惟} f (x, y) d A,$
${鈭�}_{0}^{2} {鈭�}_{0}^{- y + 2} f (x, y) d x d y$