Use Green's Theorem to evaluate the line integral along the given positive (* 2x²y?) dy -4x хе dx + C is the boundary of the region between the circles x2 + y2 = 1 and x2 + y2 = 9

Q: 6² F. dr using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify…

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Q: e) S(secx + cotx)* dx 2.

A: To evaluate the given integral

Q: Calculate the integral O (y – e*) dx + (3x + e') dy where L is along the curve x + y´ : = /x2 + y² -…

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Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two…

A: The given vector is F=3x2yi+x3j Here we use Green's theorem. So the Green's theorem is…

Q: Use the Fundamental Theorem of Line Integrals to calculate 7. di exactly. F6 sin(6x + y)i + sin(6x +…

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Q: a) Plot a direction field and some integral curves  for xy'-2y=-1 on the rectangular region {-1<or…

A: a) given differential equation  xy'-2y=-1 claim- plot a direction field and sole integral curves for…

Q: Let F = 10xe³i+ 5x²e³ j and Ğ = 10(x − y)i + 5(x + y) j. Let C' be the path consisting of lines from…

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Q: We will try to compute the real integrale-1²/²e-itz dr. Let R> 0 and let y be the rectangle with…

A: As per the question we are given an improper Integral whose value we have to find by finding : The…