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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:

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:

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Solution

In the given double integral, โˆซโˆซ๐ท(2๐‘Ž๐‘ฅ3๐‘ฆโˆ’5๐‘ฆ2)๐‘‘๐‘ฆ๐‘‘๐‘ฅ, the constants during the first integration (with respect to y) are the terms that do not involve y.

Here, the only term that does not involve y is 2๐‘Ž๐‘ฅ3. However, this term is multiplied by y in the integrand, so there are no constants during the first integration.

In other words, all terms in the integrand are functions of y, so there are no constants when integrating with respect to y.

This problem has been solved

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