In the integral, ∫∫𝐷(2𝑎𝑥3𝑦−5𝑦2)𝑑𝑦𝑑𝑥, where 𝐷is the region the integral is to be evaluated, tthe constants during the first integration is/are:

Question

In the integral, $\int\int_{D}(2a x^{3} y - 5y^{2}) \, dy \, dx$ ,

where $D$ is the region the integral is to be evaluated, the constants during the first integration is/are:

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Solution

In the given double integral, ∫∫𝐷(2𝑎𝑥3𝑦−5𝑦2)𝑑𝑦𝑑𝑥, 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 2𝑎𝑥3. 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.

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In the integral, ∫∫𝐷(2𝑎𝑥3𝑦−5𝑦2)𝑑𝑦𝑑𝑥, where 𝐷is the region the integral is to be evaluated, tthe constants during the first integration is/are:

Question

In the integral, ∫∫D(2ax3y−5y2) dy dx \int\int_{D}(2a x^{3} y - 5y^{2}) \, dy \, dx ∫∫D​(2ax3y−5y2)dydx,

Solution

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In the integral, $\int\int_{D}(2a x^{3} y - 5y^{2}) \, dy \, dx$ ,