Knowee
Questions
Features
Study Tools

Which of the following properties is not applicable to double integrals:ย โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ and โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘”(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ? Note: ๐‘Ž,๐‘,๐‘˜and๐‘™ are all constants.ย Group of answer choicesโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘˜๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=๐‘˜โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=โˆซ๐‘ฅ2๐‘ฅโˆซ๐‘Ž๐‘๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ+โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)+๐‘”(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘˜๐‘“(๐‘ฅ,๐‘ฆ)+๐‘™๐‘”(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=๐‘˜โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ+๐‘™โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ PreviousNext Not saved Submit QuizQuestionsAnsweredQuestion 1AnsweredQuestion 2AnsweredQuestion 3Haven't Answered YetQuestion 4Haven't Answered YetQuestion 5Haven't Answered YetQuestion 6Haven't Answered YetQuestion 7Haven't Answered YetQuestion 8Haven't Answered YetQuestion 9Haven't Answered YetQuestion 10Haven't Answered YetQuestion 11Haven't Answered YetQuestion 12Haven't Answered YetQuestion 13Haven't Answered YetQuestion 14Haven't Answered YetQuestion 15Haven't Answered YetQuestion 16Haven't Answered YetQuestion 17Haven't Answered YetQuestion 18Haven't Answered YetQuestion 19AnsweredQuestion 20AnsweredQuestion 21AnsweredQuestion 22AnsweredQuestion 23AnsweredQuestion 24Time Running:Hide TimeAttempt due: Aug 5 at 11:59pm

Question

Which of the following properties is not applicable to double integrals:ย โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ and โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘”(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ? Note: ๐‘Ž,๐‘,๐‘˜and๐‘™ are all constants.ย Group of answer choicesโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘˜๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=๐‘˜โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=โˆซ๐‘ฅ2๐‘ฅโˆซ๐‘Ž๐‘๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ+โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)+๐‘”(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘˜๐‘“(๐‘ฅ,๐‘ฆ)+๐‘™๐‘”(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=๐‘˜โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ+๐‘™โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ PreviousNext Not saved Submit QuizQuestionsAnsweredQuestion 1AnsweredQuestion 2AnsweredQuestion 3Haven't Answered YetQuestion 4Haven't Answered YetQuestion 5Haven't Answered YetQuestion 6Haven't Answered YetQuestion 7Haven't Answered YetQuestion 8Haven't Answered YetQuestion 9Haven't Answered YetQuestion 10Haven't Answered YetQuestion 11Haven't Answered YetQuestion 12Haven't Answered YetQuestion 13Haven't Answered YetQuestion 14Haven't Answered YetQuestion 15Haven't Answered YetQuestion 16Haven't Answered YetQuestion 17Haven't Answered YetQuestion 18Haven't Answered YetQuestion 19AnsweredQuestion 20AnsweredQuestion 21AnsweredQuestion 22AnsweredQuestion 23AnsweredQuestion 24Time Running:Hide TimeAttempt due: Aug 5 at 11:59pm

...expand
๐Ÿง Not the exact question you are looking for?Go ask a question

Solution

The property that is not applicable to double integrals is:

โˆซ๐‘Ž๐‘โˆซ๐‘ฅ2๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ=โˆซ๐‘ฅ2๐‘ฅโˆซ๐‘Ž๐‘๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅ

This is because the order of integration matters in double integrals. You cannot simply switch the order of the integrals without changing the limits of integration. The other properties listed are valid for double integrals.

Similar Questions

For the double integral:ย โˆซ09โˆซ0๐‘ฅ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅIf the differential element used is ๐‘‘๐‘ฅ๐‘‘๐‘ฆ, the integral becomes:ย Group of answer choicesโˆซ03โˆซ๐‘ฆ29๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ03โˆซ9๐‘ฆ2๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ03โˆซ0๐‘ฆ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ09โˆซ0๐‘ฆ๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฅ๐‘‘๐‘ฆ PreviousNext

Which of the following is a double integral evaluated on a region bounded by the curves ๐‘ฅ2+4๐‘ฆ2=4 and ๐‘ฅ+2๐‘ฆ=2 in the first quadrant?ย Group of answer choicesโˆซ01โˆซ2โˆ’2๐‘ฆ4โˆ’4๐‘ฆ2๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ02โˆซ1โˆ’๐‘ฅ24โˆ’๐‘ฅ22๐‘“(๐‘ฅ,๐‘ฆ)๐‘‘๐‘ฆ๐‘‘๐‘ฅNone of theseBoth integrals

Which of the following isย  a valid double integral?ย Group of answer choicesโˆซ05โˆซ3๐‘ฆ๐‘’3๐‘ฅ๐‘‘๐‘ฆ๐‘‘๐‘ฅโˆซ0๐‘ฅโˆซ324๐‘ฅ๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ04โˆซ33๐‘ฅ๐‘’3๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ01โˆซ3๐‘’๐‘ฆ4๐‘ฅ๐‘‘๐‘ฅ๐‘‘๐‘ฆ PreviousNext

For the triple integral:ย โˆซ0๐‘Žโˆซ04๐‘ฆโˆซ0๐‘”(๐‘ฅ,๐‘ฆ)๐‘“(๐‘ฅ,๐‘ฆ,๐‘ง)๐‘‘๐‘ง๐‘‘๐‘ฅ๐‘‘๐‘ฆwhat is the order at which the integral should be evaluated?ย Group of answer choiceswith respect to x then y then zwith respect to z then y then xwith respect to z then x then ywith respect to y then x then z

In the integral, โˆซโˆซ๐ท(2๐‘Ž๐‘ฅ3๐‘ฆโˆ’5๐‘ฆ2)๐‘‘๐‘ฆ๐‘‘๐‘ฅ,ย  where ๐ทis the region the integral is to be evaluated, tthe constants during the first integration is/are:Group of answer choicesx and yonly aa and xa and y

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.