Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices (0,0); (4,0) and (4,4)

Q: 2) Use Green's Theorem to compute f F df where F= (3x +4y)i + 2xyj and C is the triangular path from…

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Q: fy the notation that shows the transformation of triangle SML onto triangle S'M'L' to show the…

A: Explanation and solutions is given below....

Q: Use a projection to derive a formula for the distance from a point (x,y) to the line ax+by=c, where…

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Q: Show that (x, y) = 5x1y1 – 9x2y2 for vectors x = (x1, x2) and y = (y1, y2) in R2 defines an inner…

A: This question is about application of linear algebra

Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

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Q: Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2), (0, 2). Use Green's…

A: Introduction: According to Green's Theorem, a line integral of a vector over a closed curve C…

Q: (x² + xy) dx + (y² - xy) dy; C: the line y = x from the origin to the point (2, 2).

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Q: Use Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle…

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Q: Consider that C is a curve given by the triangle of vertices (0,0), (2,0) and (2,1), oriented…

A: We will evaluate the given integral.

Q: Compute the line integral: y² dx + x² dy two ways. C

A: We have an line integralTo evaluate the line integral by two methods (a) By  Green theorem(b) By,…

Q: Evaluate F.dr where F(x, v) yi+ejand C is the line segment from (2, 0) to (4,0). a) 0 b) 2 c) - 2 d)…

A: Try to identify line segment then apply on integral part

Q: Show that the function given by f(x,y)= x² + 3xy is differentiable at every poin using the…

A: Introduction: Distinctiveness (differentiability) implies continuity. If a function is…

Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: ented square v V , (0, 1). The va + 8x² y dy)

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Q: Let S = Þ (D), where D = {(u, v) : u² + v² ≤ 1, u ≥ 0, v ≥ 0} and Þ (u, v) = (2u+1, uv, 3u + v). (a)…

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Q: Let C be the positively oriented square with vertices (0, 0), (2,0). (2, 2). (0, 2). Use Green's…

A: Green's Theorem:  For a positively oriented curve C∫CP dx+Q dy=∫∫D∂Q∂x-∂P∂y dAfor the region D…

Q: Evaluate the integral 108 - 2y/E+ 4ydzdy, 4 where A is the parallelogram with vertices (0,0), (),…

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Q: Jo F dr, where F = (3-2y, x-1, -2z) and C is the boundary of a triangle with vertices (0, 0, -3),…

A: Given F=3-2y, x-1, -2z C is the boundary of a triangle with vertices (0, 0, -3), (0, 4, 5), (2, 0,…

Q: Show that 7(u, v)= (²-²,2ue) maps the triangle-((u, v):05≤SS 3) to the domain D bounded by z = 0, y…

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Q: Let f(x, y, z) = eª + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A: Given: The function is fx,y,z=ex+zy2 and let C be a straight line that will connect the points 4,2,1…