JaD x dy a) Calculate the line integral along the level area D = {(x, y) = R² | 0 ≤ y ≤1 − x²} edge oD in the positive direction of rotation, i.e. "counter-clockwise". In general: In the positive rotation direction of the edge, area D remains on the left side. Tip: The edge consists of two different parts, which must be parameterized and integrated separately. For the upper edge, it is probably easiest to use the result of task 4, which also applies to parameter intervals other than [0, 1]. b) Calculate the area of the set D and compare it with the result of part a).

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
ƏD
x dy
a) Calculate the line integral
along the level area
D = {(x, y) = R² | 0 ≤ y ≤1 − x²}
-
edge dD in the positive direction of rotation, i.e. "counter-clockwise".
In general: In the positive rotation direction of the edge, area D remains on the left side.
Tip: The edge consists of two different parts, which must be parameterized and integrated
separately. For the upper edge, it is probably easiest to use the result of task 4, which also applies
to parameter intervals other than [0, 1].
b) Calculate the area of the set D and compare it with the result of part a).
Transcribed Image Text:ƏD x dy a) Calculate the line integral along the level area D = {(x, y) = R² | 0 ≤ y ≤1 − x²} - edge dD in the positive direction of rotation, i.e. "counter-clockwise". In general: In the positive rotation direction of the edge, area D remains on the left side. Tip: The edge consists of two different parts, which must be parameterized and integrated separately. For the upper edge, it is probably easiest to use the result of task 4, which also applies to parameter intervals other than [0, 1]. b) Calculate the area of the set D and compare it with the result of part a).
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