?Use Green's Theorem to evaluate. (Check the orientation \(\int_{c_{1}} F_{1} \cdot d

Chapter 14, Problem 15

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QUESTION:

Use Green's Theorem to evaluate. (Check the orientation \(\int_{c_{1}} F_{1} \cdot d r\) of the curve before applying the theorem.)

\(F(x, y)=\langle y \cos x-x y \sin x, x y+x \cos x\rangle\),
\(C\) is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0)

Equation Transcription:

 〈

Text Transcription:

int_{C_1} F . dr

F(x, y) = left angle y cos x - x y sin x, x y + x cos x right angle

C

Questions & Answers

QUESTION:

Use Green's Theorem to evaluate. (Check the orientation \(\int_{c_{1}} F_{1} \cdot d r\) of the curve before applying the theorem.)

\(F(x, y)=\langle y \cos x-x y \sin x, x y+x \cos x\rangle\),
\(C\) is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0)

Equation Transcription:

 〈

Text Transcription:

int_{C_1} F . dr

F(x, y) = left angle y cos x - x y sin x, x y + x cos x right angle

C

ANSWER:

Step 1 of 3

Consider the given triangle with points  

Find the equation of line using the two points 

Recall that the equation of line with two points  and  is given as

This gives the equation of line:

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