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Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy - 5yzª dz

Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) (0,0,0) 4x³y dx + (x²-25) dy - 5yzª dz

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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Question
Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Ta (0,0,0) 4x³y dx + (x² -25) dy - 5yz* dz
Transcribed Image Text:Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Ta (0,0,0) 4x³y dx + (x² -25) dy - 5yz* dz
Although it is not defined on all of space R³, the field associated with the line integral below is defined on a region that is simply connected, and the component test can be used to show it is conservative. Find a potential function for the field and evaluate the integral. (4,4,4) (3,3,3) * - - - * - * dy dz
Transcribed Image Text:Although it is not defined on all of space R³, the field associated with the line integral below is defined on a region that is simply connected, and the component test can be used to show it is conservative. Find a potential function for the field and evaluate the integral. (4,4,4) (3,3,3) * - - - * - * dy dz
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