Area line integral Show that the value of xy² dx + (x²y + 2x) dy depends only on the area of the region enclosed by C.
Area line integral Show that the value of xy² dx + (x²y + 2x) dy depends only on the area of the region enclosed by C.
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
Transcribed Image Text:Area line integral Show that the value of
xy² dx + (x²y + 2x) dy
depends only on the area of the region enclosed by C.
Expert Solution
Step 1
We know that the area bounded by the curves is evaluated using the double integral formula which
is , where R is the region of integration.
We can write the given integral , where M and N are the
components of a vector field such that and .
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