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?Use Green's Theorem to evaluate\(\int_{C} F \cdot d r\). (Check the orientation of the
Chapter 14, Problem 16(choose chapter or problem)
Use Green's Theorem to evaluate\(\int_{C} F \cdot d r\). (Check the orientation of the curve before applying the theorem.)
\(F(x, y)=\left\langle e^{-x}+y^{2}, e^{-y}+x^{2}\right\rangle\),
\(C\) consists of the arc of the curve \(y=\cos x\) from \((-\pi / 2,0)\) to \((\pi / 2,0)\) and the line segment from \((\pi / 2,0)\) to \((-\pi / 2,0)\)
Equation Transcription:
〈
⟩
Text Transcription:
int_C F . dr
(F(x, y)= left angle e^-x + y^2, e^-y + x^2 rightrangle
C
y = cos x
(-pi/2)
(pi/2)
(pi/2)
(-pi/2)
Questions & Answers
QUESTION:
Use Green's Theorem to evaluate\(\int_{C} F \cdot d r\). (Check the orientation of the curve before applying the theorem.)
\(F(x, y)=\left\langle e^{-x}+y^{2}, e^{-y}+x^{2}\right\rangle\),
\(C\) consists of the arc of the curve \(y=\cos x\) from \((-\pi / 2,0)\) to \((\pi / 2,0)\) and the line segment from \((\pi / 2,0)\) to \((-\pi / 2,0)\)
Equation Transcription:
〈
⟩
Text Transcription:
int_C F . dr
(F(x, y)= left angle e^-x + y^2, e^-y + x^2 rightrangle
C
y = cos x
(-pi/2)
(pi/2)
(pi/2)
(-pi/2)
ANSWER:
Step 1 of 2
One needs to find following integral:
\(\int _C\text{Pdx}+\text{Qdy}=\int_C\left ( \text{x}^{2/3}+\text{y}^2 \right )\text{dx}+\left ( \text{y}^{4/3}-\text{x}^2 \right )\text{dy}\)
Taking partial derivative of function,
Therefore,
