In the integral, โซโซ๐ท(2๐๐ฅ3๐ฆโ5๐ฆ2)๐๐ฆ๐๐ฅ,ย where ๐ทis 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, โซโซ๐ท(2๐๐ฅ3๐ฆโ5๐ฆ2)๐๐ฆ๐๐ฅ,ย where ๐ทis 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
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.
Similar Questions
In the integral, โซโซ๐ท(2๐๐ฅ3๐ฆโ5๐ฆ2)๐๐ฆ๐๐ฅ,ย where ๐ทis the region the integral is to be evaluated, tthe constants during the first integration is/are:
For the double integral:ย โซ09โซ0๐ฅ๐(๐ฅ,๐ฆ)๐๐ฆ๐๐ฅIf the differential element used is ๐๐ฅ๐๐ฆ, the integral becomes:ย Group of answer choicesโซ03โซ๐ฆ29๐(๐ฅ,๐ฆ)๐๐ฅ๐๐ฆโซ03โซ9๐ฆ2๐(๐ฅ,๐ฆ)๐๐ฅ๐๐ฆโซ03โซ0๐ฆ๐(๐ฅ,๐ฆ)๐๐ฅ๐๐ฆโซ09โซ0๐ฆ๐(๐ฅ,๐ฆ)๐๐ฅ๐๐ฆ PreviousNext
1. Evaluate the following integrals a. โซ โ๐ฅ๐๏ฟฝ
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