Calculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with vertices (2, −4), (2, -3), (−3,−3), and (−3,-4) oriented clockwise. Enter an exact answer. Provide your answer below: f(3x³ 4x + 4y + 8) dx + (−3xy + 5) dy =
Calculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with vertices (2, −4), (2, -3), (−3,−3), and (−3,-4) oriented clockwise. Enter an exact answer. Provide your answer below: f(3x³ 4x + 4y + 8) dx + (−3xy + 5) dy =
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
![**Calculate the line integral**
\[ \oint_{C} (3xy^3 - 4x + 4y + 8) \, dx + (-3xy + 5) \, dy, \]
where \( C \) is the rectangle with vertices \( (2, -4), (2, -3), (-3, -3), \) and \( (-3, -4) \) oriented clockwise. Enter an exact answer.
**Provide your answer below:**
\[ \oint_{C} (3xy^3 - 4x + 4y + 8) \, dx + (-3xy + 5) \, dy = \boxed{} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13d2fa52-7679-4dbf-8ccf-e0669bc97f10%2F6a98470a-6054-4dfb-a005-7fa8ae0a9df5%2Fn1i2q3g_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculate the line integral**
\[ \oint_{C} (3xy^3 - 4x + 4y + 8) \, dx + (-3xy + 5) \, dy, \]
where \( C \) is the rectangle with vertices \( (2, -4), (2, -3), (-3, -3), \) and \( (-3, -4) \) oriented clockwise. Enter an exact answer.
**Provide your answer below:**
\[ \oint_{C} (3xy^3 - 4x + 4y + 8) \, dx + (-3xy + 5) \, dy = \boxed{} \]
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