Knowee
Questions
Features
Study Tools

If the order of integration is reversed for the double integral ย โˆซโˆ’11โˆซ๐‘ฅ21๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฆ๐‘‘๐‘ฅ, theย  integral will become _____.ย Group of answer choicesโˆซ02โˆซโˆ’๐‘ฆ๐‘ฆ๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ01โˆซโˆ’๐‘ฆ๐‘ฆ๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆNone of theseโˆซ๐‘ฅ21โˆซโˆ’11๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆ PreviousNext

Question

If the order of integration is reversed for the double integral ย โˆซโˆ’11โˆซ๐‘ฅ21๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฆ๐‘‘๐‘ฅ, theย  integral will become _____.ย Group of answer choicesโˆซ02โˆซโˆ’๐‘ฆ๐‘ฆ๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆโˆซ01โˆซโˆ’๐‘ฆ๐‘ฆ๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆNone of theseโˆซ๐‘ฅ21โˆซโˆ’11๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆ PreviousNext

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

Solution

The integral will become โˆซ01โˆซโˆ’๐‘ฆ๐‘ฆ๐‘’๐‘ฅ+๐‘ฆ๐‘‘๐‘ฅ๐‘‘๐‘ฆ.

Here's why:

The original limits of integration for the inner integral are from x to 2. This means that y varies from x to 2. For the outer integral, the limits are from -1 to 1, which means x varies from -1 to 1.

When we reverse the order of integration, we need to express x in terms of y. Looking at the original limits, we can see that x varies from -y to y. The limits for y are from 0 to 1.

So, the new limits of integration will be โˆซ01โˆซโˆ’๐‘ฆ๐‘ฆ for the double integral.

This problem has been solved

Similar Questions

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

Change the order of integral and hence evaluateโˆซ โˆซ เฏฌเฐฎเฏ—เฏซเฏ—เฏฌเถฅเฏฌเฐฐเฌฟเฏ”เฐฎเฏซเฐฎเฏ”โˆšเฏ”เฏซเฏ”เฌด

Using the change of coordinate system, the integralย  ย โˆซ01โˆซ01โˆ’๐‘ฅ2(๐‘ฅ2+๐‘ฆ2)๐‘‘๐‘ฆ๐‘‘๐‘ฅ would then take the form ______.Group of answer choicesโˆซ0๐œ‹4โˆซ01๐‘Ÿ2๐‘‘๐‘Ÿ๐‘‘๐œƒโˆซ0๐œ‹2โˆซ01๐‘Ÿ2๐‘‘๐‘Ÿ๐‘‘๐œƒโˆซ0๐œ‹4โˆซ01๐‘Ÿ3๐‘‘๐‘Ÿ๐‘‘๐œƒโˆซ0๐œ‹2โˆซ01๐‘Ÿ3๐‘‘๐‘Ÿ๐‘‘๐œƒ PreviousNext

What form does this integral take if its order of integration is reversed?

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

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.