05||Techniques for Evaluating Variable Limit Double Integrals ||Integral Calculus||Dr Prashant Patil

This video tutorial demonstrates the step-by-step evaluation of a double integral where the inner limits are defined as a function of a variable. The instructor explains that because the inner boundary is defined by y equaling x squared, the integration must prioritize the variable y first, even if the differential order suggests otherwise. Throughout the process, the teacher treats the variable x as a constant during the initial integration phase before substituting the upper and lower limits. After reducing the expression to a single variable, the final calculation is performed with respect to x to reach a numerical solution. This instructional guide emphasizes the importance of correctly identifying the order of integration based on the provided mathematical boundaries. #DrPrashantPatil#InegralCalulus#22MAT11#18MAT11#Lecture#1BMATE201 For more videos and playlist of Engineering Mathematics go through the playlists 1)18MAT41- Complex Analysis, Probability and Statistical Methods: 1) Conformal Transformations[18MAT41-Module 02] https://www.youtube.com/playlist?list=PL1g2IG9eNHztfVyDfC_qYBldBbW6pLuvI 2) Complex Integration[18MAT41-Module 02] https://www.youtube.com/playlist?list=PL1g2IG9eNHztjcUm7OvXC7JF615VP37rX 3) Probability Distributions[18MAT41-Module 03] https://www.youtube.com/playlist?list=PL1g2IG9eNHztiKVyLOT59ikagyneujbUA 4) Joint Probability Distribution and Sampling [18MAT41-Module 05] https://www.youtube.com/playlist?list=PL1g2IG9eNHzu8a9wzp3PtJNJ8X_Q9fqU6 2) 18MAT31- TRANSFORM CALCULUS, FOURIER SERIES AND NUMERICAL TECHNIQUES: 1) Laplace Transforms [18MAT31-Module 01]: https://www.youtube.com/playlist?list=PL1g2IG9eNHzsFyqJxBws2aZaJLB8hya8O 2) Inverse Laplace Transform [18MAT31-Module 01]: https://www.youtube.com/playlist?list=PL1g2IG9eNHzv0m4Z3NGPX2I8hNFANcv_p 3) Fourier Series | 18mat31 | Module 02 | Dr Prashant Patil https://www.youtube.com/playlist?list=PL1g2IG9eNHzuVzlVnbb_EsCc5t3pOg5Gv 3) Fourier Transforms | 18mat31 | Module 03 | Dr Prashant Patil https://youtube.com/playlist?list=PL1g2IG9eNHzsLt3xCgokFOk44SG9laz6J 4) Numerical Methods for ODE | 18mat31 | Module 04 & 05 | Dr Prashant Patil https://youtube.com/playlist?list=PL1g2IG9eNHzvHY-tA51PlwFsP1s5Qwr3E 5) Calculus of Variations | 18mat31 | Module 05 | Dr Prashant Patil https://youtube.com/playlist?list=PL1g2IG9eNHzs_1mpsKQ1NMiFBQhF5XqtT 2)18MAT21- Advanced Calculus and Numerical Techniques: 1) Vector Calculus [18MAT21-Module 01]: https://www.youtube.com/playlist?list=PL1g2IG9eNHzsJ2wXNQ976nIUbr2f_3xb2 2) Ordinary Differential Equation of Higher order[18MAT21-Module 02]: https://www.youtube.com/playlist?list=PL1g2IG9eNHzutcFjyVlDQb9fGdUTYsU-d 3) Partial Differential Equations [18MAT21-Module 03]: https://www.youtube.com/playlist?list=PL1g2IG9eNHzu1Bobeh2ydpJERhlsJg84z 4) Infinite Series [18MAT21-Module 04]: https://www.youtube.com/playlist?list=PL1g2IG9eNHztQXrB5uGwwqPJaTOOiuh2E 4)18MATDIP41- Additional Mathematics II: 1) Probability[18MATDIP41-Module05] https://www.youtube.com/playlist?list=PL1g2IG9eNHztgrose3lcbZCMMjoC_mVk2