#1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and (1,7) by making an appro- priate change of variables to obtain an integral over the square S with vertices (0,0), (1,0), (0,1) and (1, 1).

Q: 21. Let D be the parallelogram in Figure 13. Apply the Change of Variables Formula to the map G(u,…

A: Given first find out

Q: In this problem we use the change of variables r = 3s + t, y = s - 2t to compute the integral SR(x +…

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Q: 4. Calculate the integral (x – 3y) dA where R is the triangular region with vertices (0,0), (2, 1)…

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Q: Refer to V=C[0,1], with the inner product given by an integral. Compute (f.g), where f(t) = 16t – 12…

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Q: 2. Evaluate the given line integral, | (-y,x – y) · dR, where C is the line segment from (1,0) to…

A: To find the line integral we use the equation of line segment in parametric form using given points.

Q: (a) Let F = 4x27 + y} - (z – 1)k. Compute I7. dA where S is a square of side 5 units centered at…

A: Given that, the vector is F→=4x2i→+yj→-z-1k→. Determine the value of ∫SF→·dA→.…

Q: fo F(1+ 2t, 1+ 3t)dt is equivalent to the line integral of F(x, y) on the line segment from (1,1) to…

A: Here we have to find is the given statement is true or false

Q: 1 1 Use the transformation u = 2x + y, v = x+ 2y to evaluate the given integral for the region…

A: Integration by transforming variables.

Q: .Find the exact value of the double integral. J (2x + 5y) dA, where R is the rectangular region…

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Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

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Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1, 0) to…

A: Introduction: The formula of line integral of the function f(x,y) on the line segment C(t) is given…

Q: Calculate the Line Integral for the F(x,y) = 6 – 3x – 2y where the boundary curve is C: x^2+4y^2=9

A: F(x,y) = 6 – 3x – 2y  To Find: Calculate the Line Integral for the F(x,y) where the boundary curve…

Q: (2) Find the work done by F(x, y) = (2xy³, 4x²y²) moving a particle on the path C where C is the…

A: Formula: Work done W by a force field F on a particle on the path C is: W=∫C F·dr It is given that…

Q: Evaluate the triple integral. 16.  ∫∫∫T  xz dV , where T is the solid tetrahedron with vertices…

A: The solid tetrahedron T with vertices 0, 0, 0, (1, 0, 1), (0, 1 ,1) and 0,0, 1. The solid region is…

Q: 17. Find the exact area of the surface z = 1 + 2x + 3y + 4y2, 1x 4, 0 y < 1

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Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

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Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: 5. Evaluate the line integral (r+2y) dr+x² dy where C consists of line segments from (0,0) to (2, 1)…

A: In order to solve this question by the formula of line integral .

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: If F = (2z+ y,z, 2y+x) and S is a unit square in the yz-plane with its normal in the positive…

A: Consider the given vector F.

Q: Find the absolute maximum and minimum values of f(x, y) = 3xy−6x−3y + 7 on the closed triangular…

A: Find out the absolute maximum and minimum values of  f(x,y)=3xy-6x-3y+7 for the maximum and minimum…

Q: (z+ y – 1) cos D

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Q: Set up an integral for the length of y = vx + 2, 2 2 <x<7 using ds = 1+ ) dy. A. ds = f, /1+ 4y²dy…

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Q: 10.18. Use an appropriate change of variables to evaluate the integral ff,(1 + x? + y²)²dA, where T…

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Q: 1. Evaluate the line integral f(z, y) ds where f(x, y) = Vx+ 2y and C is the straight-line segment…

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Q: Use the given transformation to evaluate the integral. 3x dx dy, u = x+ y, v = - 2x+y where R is the…

A: To evaluate the double integral using change of variable follow: Determine the region under a given…

Q: Verify the Green's theorem for integral x²y dx + xy dy, where C is the boundary described…

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Q: Evaluate the double integral. I1, 7y? dA, D is the triangular region with vertices (0, 1), (1, 2),…

A: We need to find  double integral , ∫∫D7y2dA  , where D is the triangular region with vertices (0 ,…

Q: 2. In A ABC, X is the centroid. A A If CW = 15, find cx and XW. W, B. If BX = 8, find BY and XY.

A: we know that  centroid is located 23 of the distance from the vertex along the segment that connects…

Q: (b) ſf f(x,y) dA if f(x, y) = y², where R is the triangular region with vertices (0, 1), (1, 2) and…

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Q: 3. Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0),…

A: Solution is below

Q: 2. Let C be the positively oriented boundary of the square whose sides lie along the lines r ±1 and…

A: According to cauchy’s integral formula for any region C,

Q: 5) Evaluate the line integral S YX²dX + XY²dY on curve C, where C is the upper portion of the www m…

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Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

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Q: 8. Evaluate the line integral x dx + xedy where C is the closed path along the triangle in the…

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Q: Suppose we have a surface f (x,y)=x²y+cos (4x) · Which of the following is the gradient of f(x,y) at…

A: First I have found the partial derivatives of f(x,y)  with respect to 'x' and 'y' at point P(π/2,…

Q: 3.4.6 Use Green's theorem in a plane to evaluate of 10x9²³- [(xy²-y) dx + (x + y²) dy] C as a double…

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Q: Find c'(t) and ||c'(t) || - c'(t) = (2e',41,2) (2e*, 4t, 2) ||c'(t)|| = V 4e + 4t + 4| 2t 4²? - 4e2t…

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Q: 1 Find the centroid of the area bounded by x2- 4y + 8 = 0, the lines x = 0 and x = 4, and the…

A: Formulas are written within the solution.

Q: (6) Evaluate the line integral / r²ydx + xy°dy, where C is the square with vertices (0,0), (1,0),…

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Q: Suppose F(x,y)=(4x+6y)i +(6x+4y)j. Evaluate the line integral for each of the given paths, which are…

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Q: Consider the following. Z = =DVx²+ y?, 5x - 2y + 3z = 22, (3, 4, 5) (a) Find symmetric equations of…

A: a) Here, f(x,y,z)≡x2+y2-z2=0g(x,y,z)≡5x-2y+3z=22P≡(3,4,5)

Q: In this problem we use the change of variables a = 4s +t, y = s – 3t to compute the integral fa (* +…

A: Given: The change of variable is given as, x=4s+t y=x-3t The vertices of parallelogram is…

Q: Q#03(a): Use Green's theorem to evaluate the line integral f. (x – 3y) dx (4x + y) dy, where C is…

A: Green's theorem

Q: 3.4.6 Evaluate the line integral I = =f( (xy dx + x dy) C where C is the closed curve consisting of…

A: We have to solve the given problem

Q: 8. Evaluate the line integral (x'dx+ xe"dy where C is the closed path along the triangle in the…

A: Here we have to evaluate the integral ∫cx2dx+xe-ydy where C is the closed path along the triangle in…

Q: 3. Set up the integral to find fffr x dV where T is the tetrahedron in the first octant under the…

A: To set up the integral to find ∭TxdV

Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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