Question

1. Evaluate the line integral by two methods:(a) directly and (b) using Green's Theorem. ?_C x dx + y dy, C consists of the line segments from (0,1) to (0,0) and from (0,0) to (1,0) and the parabola y = 1 - x^2 from (1,0) to (0,1)

          1. Evaluate the line integral by two methods:(a) directly and (b) using Green's Theorem.
?_C x dx + y dy, C consists of the line segments from (0,1) to (0,0) and from (0,0) to (1,0) and the parabola y = 1 - x^2 from (1,0) to (0,1)

1. Evaluate the line integral by two methods:(a) directly and (b) using Green's Theorem.
?C x dx + y dy, C consists of the line segments from (0,1) to (0,0) and from (0,0) to (1,0) and the parabola y = 1 - x^2 from (1,0) to (0,1)

Added by Francisco M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

12/13/2024

Step 1

For the first segment from (0,1) to (0,0), we have x=0 and y varies from 1 to 0. So, we can parameterize it as r(t) = (0, 1-t), where t goes from 0 to 1. For the second segment from (0,0) to (1,0), we have y=0 and x varies from 0 to 1. So, we can parameterize it Show more…

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1. Evaluate the line integral by two methods:(a) directly and (b) using Green's Theorem. ∮_C x dx + y dy, C consists of the line segments from (0,1) to (0,0) and from (0,0) to (1,0) and the parabola y = 1 - x^2 from (1,0) to (0,1)