## Question

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Change the order of integration in

\(\mathop{\int }_{0}^{a}\mathop{\int }_{y}^{a}\frac{x}{{{x}^{2}}+{{y}^{2}}}dx~dy\)

## Answer (Detailed Solution Below)

## Detailed Solution

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Concept:

In a double integral with variable limits, the change of order of integration can sometimes make the evaluation easy.

Calculation:

Since the limit of y is constant hence, we can say that a horizontal strip was taken for integration now for change of order we will take vertical strip as shown in the following diagram.

∴ \(\mathop{\int }_{0}^{a}\mathop{\int }_{0}^{x}\frac{x}{{{x}^{2}}+{{y}^{2}}}dy~dx\) is the correct solution.

Last updated on Apr 13, 2023

MPSC AE Result Out for Electrical (Advt. 089/2022)! Earlier, the interview schedule was out for Advt. 064/2022. The interview was scheduled to be conducted from 17th to 21st April and 25th to 28th April 2023. The Maharashtra Public Service Commission (MPSC) released a notification for MPSC AE Recruitment. A total number of 151 vacancies were released for Civil, Mechanical and Electrical disciplines. The application process started on 3rd October 2022 and the candidates could apply till 23rd October 2022. There are 3 stages of the selection process – Prelims, Mains and Interview. The prelims exam was held on 17th December 2022. The candidates who will get qualified in the prelims are eligible to attend the mains. The final select list will be released after the Interview.