Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the integral where C is any path from (1,0) to (2, 1).

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: F(x, y) = (2x - y, x + 3y), and let C be the path along the parabola y = 2x² from (0, 0) to (2,8).…

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Q: Vx2 (b) / 4 dx; x > 2. x2

A: To find out the integration.

Q: Without evaluating the integral, show that √ √ 2 ² 4+1 4₂ | 15 | 1/2 dz where C is the line segment…

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Q: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

Q: 3. Let C be the part of the circle with radius 3 in the first quadrant as in the picture. 3. (a)…

A: To solve the following paramteric equation problem

Q: F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b)…

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Q: What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?

A: Given:            f(x, y) = 5   over rectangle -2, 3×2, 4

Q: | 5y? dx +xy dy

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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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