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Consider the double integral (Check image for the integral) a) What difficulty arises when proceeding to carry out the calculation of the integral with the established order of differentials, that is, with the order dydx? b) Could the calculation of the integral be carried out by reversing the order of integration? Argue your answe

Consider the double integral (Check image for the integral) a) What difficulty arises when proceeding to carry out the calculation of the integral with the established order of differentials, that is, with the order dydx? b) Could the calculation of the integral be carried out by reversing the order of integration? Argue your answe

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the double integral (Check image for the integral)

a) What difficulty arises when proceeding to carry out the calculation of the integral with the established order of differentials, that is, with the order dydx?

b) Could the calculation of the integral be carried out by reversing the order of integration? Argue your answer.

11 le dydx 00
Transcribed Image Text:11 le dydx 00
Expert Solution
Step 1

(a) Since we can integrate emx but to integrate exm, we don't have any specific formula. 

So, we are unable to integrate exm.

So, it is not possible to integrate ∫01∫01e-x2-y2dydx in rectangular coordinates. But after converting the integral into polar coordinates, we can evaluate the integral.

For this purpose, substitute

 x2+y2=x2, dydx=dxdy=rdrdθ

Then, we can integrate easily for r going from 0 to 1 and θ varies from 0 to π4

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