?Use Green's Theorem to evaluate the line integral along the given positively oriented

Chapter 14, Problem 5

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QUESTION:

Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

\(\int_{c} y e^{x} d x+2 e^{x} d y\),

C is the rectangle with vertices (0,0),(3,0),(3,4), and (0,4)

Equation Transcription:

Text Transcription:

Integral_C ye^x dx + 2e^x dy

Questions & Answers

QUESTION:

Use Green's Theorem to evaluate the line integral along the given positively oriented curve.

\(\int_{c} y e^{x} d x+2 e^{x} d y\),

C is the rectangle with vertices (0,0),(3,0),(3,4), and (0,4)

Equation Transcription:

Text Transcription:

Integral_C ye^x dx + 2e^x dy

ANSWER:

Step 1 of 2

To evaluate , where is the rectangle with vertices ,,and  using Green’s Theorem.

From Green’s Theorem we have that “Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If P and Q have continuous partial derivatives on an open region that contains D, then

”.                               …… (1)

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