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13 Nov 2019
EXTRA CREDIT first need to find the suitable function which needs to be integration. Exactly same situation is going on here. We just have substituted in order to simplify the Here is a warm up question: This question familiar for the next questions. on will not be graded. But you still should do it to get be 1. Show that /(r cos θ , r sin θ)rdrd0 I secretl do the necessary calculations. y gave you the required transformation in the problem. Your goal ls vo Here comes the actual problems. I will grade these. Evaluate the integration region in the zy plane with vertices at (1,0), (2,0), (0,-2), (0,-1) Use the transformations x = to do in the ay plane. will need the transformations here and some algebra skills. u+v and y = Hint: (i) Try to realize the need of the transformation first, i.e, why the integration is difficult transformation f e Draw the region D in zy plane. Then find out how to draw the region in the u p to an integration in the uw plane and evaluate it. Check your answer get satisfied untill both of you are happy with each others work. Good (iii) Change the integration your friends. Dont luck! 2. Prove the integration conversion formulla from the rectangular coordinate to spherical coor- dinate,i.e. f(x, y, z)dzdydz- Hint: (i) I did not provide the transformation here. So you need to find that. May be your class notes from spherical coordinates will help. (Gi) If you have done the warm up question before attempting this one, you should be able to understand the striking similarity between the problems. If not, then I strongly suggest that you should go back and do that problem. Good Luck!
EXTRA CREDIT first need to find the suitable function which needs to be integration. Exactly same situation is going on here. We just have substituted in order to simplify the Here is a warm up question: This question familiar for the next questions. on will not be graded. But you still should do it to get be 1. Show that /(r cos θ , r sin θ)rdrd0 I secretl do the necessary calculations. y gave you the required transformation in the problem. Your goal ls vo Here comes the actual problems. I will grade these. Evaluate the integration region in the zy plane with vertices at (1,0), (2,0), (0,-2), (0,-1) Use the transformations x = to do in the ay plane. will need the transformations here and some algebra skills. u+v and y = Hint: (i) Try to realize the need of the transformation first, i.e, why the integration is difficult transformation f e Draw the region D in zy plane. Then find out how to draw the region in the u p to an integration in the uw plane and evaluate it. Check your answer get satisfied untill both of you are happy with each others work. Good (iii) Change the integration your friends. Dont luck! 2. Prove the integration conversion formulla from the rectangular coordinate to spherical coor- dinate,i.e. f(x, y, z)dzdydz- Hint: (i) I did not provide the transformation here. So you need to find that. May be your class notes from spherical coordinates will help. (Gi) If you have done the warm up question before attempting this one, you should be able to understand the striking similarity between the problems. If not, then I strongly suggest that you should go back and do that problem. Good Luck!
Hubert KochLv2
18 Jul 2019