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6. Let u(x, y) = Re(2²) and v(x, y) = Im(2²). Compute the line integrals in R² given by (udx - vdy) and [_(udz – vdy), where the lines & both begin and end at (x, y) = (0, 0) and (x, y) = (1, 1), but l_ travels horizontally one unit along the x-axis and then vertically one unit, while + travels vertically one unit along the y-axis and then horizon- tally one unit. Compare your two results.

6. Let u(x, y) = Re(2²) and v(x, y) = Im(2²). Compute the line integrals in R² given by (udx - vdy) and [_(udz – vdy), where the lines & both begin and end at (x, y) = (0, 0) and (x, y) = (1, 1), but l_ travels horizontally one unit along the x-axis and then vertically one unit, while + travels vertically one unit along the y-axis and then horizon- tally one unit. Compare your two results.

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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6. Let u(x, y) = Re(z²) and v(x, y) = Im(z²). Compute the line integrals in R² given by [_(uda - vdy) and [_(udx - vdy), where the lines l_ both begin and end at (x, y) = (0, 0) and (x, y) = (1, 1), but l_ travels horizontally one unit along the x-axis and then vertically one unit, while + travels vertically one unit along the y-axis and then horizon- tally one unit. Compare your two results.
Transcribed Image Text:6. Let u(x, y) = Re(z²) and v(x, y) = Im(z²). Compute the line integrals in R² given by [_(uda - vdy) and [_(udx - vdy), where the lines l_ both begin and end at (x, y) = (0, 0) and (x, y) = (1, 1), but l_ travels horizontally one unit along the x-axis and then vertically one unit, while + travels vertically one unit along the y-axis and then horizon- tally one unit. Compare your two results.
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