Evaluate the integral [₁ F. dr. F(x, y) = (x² + y) i+(6x - cos y) j where Cis the boundary of the region R that is inside the square with vertices (0, 0), (8, 0), (8, 8), (0, 8) but is outside the rectangle with vertices (1, 1), (7, 1), (7, 2), (1, 2). Assume that C' is oriented so that the region R is on the left when the boundary is traversed in the direction of its orientation. [1 F. dr = i

Q: 6- Evaluate the line integral fe F dr, where F = [ry, yz, r2] and C is the boundary of the…

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Q: Set up the integral (do not evaluate) in (u, v) coordinates to find the integral SSRx + y dA, where…

A: The given integral is ∬Rx+ydA over the region R which is a parallelogram with vertices…

Q: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

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Q: 10. Consider the double integral JR 1+x²+y²' ху dxdy. (a) Evaluate the integral where R is the…

A: step:-1 Given integral is ∫∫R xy1+x2+y2dxdy Part (A):-  vertices A1, 0, B5, 0, C7, 3  Now, equation…

Q: Which of the following integral is the integral f SR elz+)/(z-v)dA where R is the trapezoidal region…

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Q: Evaluate the integral F· dr. F(x, y) = (7x2 + y) i + (8x – cos y) j where Cis the boundary of the…

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Q: Let D be the triangular region in the uv-plane with vertices (0, 1), (4, 1), (1, 3) and let G(u, v)…

A: Given :-  Let D be the triangular region in the u-v plane with vertices  0, 1 ,  4 , 1 ,  1, 3. Let…

Q: Evaluate the double integral  SSDxydA where D is the triangular region with the vertices (0,0)…

A: ∬DxydA, where D is triangular region with vertices (0,0), (3,0) and (0,1).

Q: 3) Evaluate the double integral fS, dr dy where D is the region bounded by the hyperbolas ry = 2, ry…

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Q: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant…

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Q: "1₁ f(x, y) = sin(y) and D is the triangular region with vertices (0, 0), (0, 4), and (4, 0)…

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Q: Q.1A) Express integral I y + x 4x-2y) =0, x= 1 and y=0,y-1-xto T. of u = dydx in terms of (u)and…

A: The given integral is                          ∬Ry+x-4x-2y2-412dy dx where R: x=0, x=1 and y=0,…

Q: 1. Evaluate the integral [dx A S dx Ady + 3dx ^ dz of the 2-form w=dx^dy+3dx^dz over the oriented…

A: We have to find the value of integral.

Q: A region R consists of a square bounded by the lines x = -5, x = 5, y = 0, and y = -10 and a half…

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Q: Justify the Fundamental Theorem of Line Integrals for F. dr in the case when F(x, y) = (8x + 8y)i +…

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Q: 1 = √√√₁₂² xy dA, where D is the triangular region with vertices (0, 0), (6, 0), (0, 1). Evaluate…

A: To Evaluate: I=∬Dxy dA where the D is the triangular region with vertices (0,0), (6,0), and (0,1).

Q: vertices (1,0), (2,0), (0,-2) and (0,-1), by changing variables of the integral by using the and…

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Q: Evaluate the integral F· dr. F(x, y) : (7x² + y) i + (8x – cos y) j where C'is the boundary of the…

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Q: Ex,y) de by dividing the rectangle R with vertices (0, 0), (4,0), (4, 23, and (0, 2) into eight…

A: The image of rectangle can be drawn with the given coordinates.

Q: The substitution = 2x -y and v= x + y make the region R (see figure) into a simple region S in the…

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Q: Evaluate the line integral y² dx + 2x dy + dz, where C connects (0,0,0) with (1, 1, 1), (a) along…

A: We have to find out the integral value .