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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

Question

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

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Solution

The constants during the first integration are a and x.

Here's why:

The integral is a double integral, and the order of integration is dydx. This means that we first integrate with respect to y, treating all other variables as constants, and then integrate the result with respect to x.

In the integrand, 2ax^3y - 5y^2, the variables are a, x, and y. However, since we're first integrating with respect to y, we treat a and x as constants during this first integration.

So, the correct answer is a and x.

This problem has been solved

Similar Questions

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:

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. Evaluate the following integrals a. โˆซ โˆš๐‘ฅ๐‘‘๏ฟฝ

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

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