. Evaluate the line integral where F x² + y² = 4 in Q1, Q2, and Q3. - (1, 2y) and the pathway C is the three-quarter circle x,

Q: 7. Find the line tangent to the intersection of the surfaces and at the point (√2, 1, -2). x² + y²…

A: Let the equation of the first surface is                                        fx,y = x2 + y2 + z2…

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

A:

Q: Let F = (y – x, ry) and let C be the line segment from (2, –3) to (1, –1). %3D Evaluate F. dr.

A: We wil first equation of parametric equation of line segment

Q: Evaluate the line integral f3y² dx + z² dy + (16 - x²) dz over the quarter of the circle of radius 4…

A: Kindly refer to Step 2 for the solution.

Q: Evaluate the line integral xdy- xydx over the closed path C where Cis the circle C

A:

Q: 8. Which of the following is the curl of F = (2xy +1, x² + 2yz, y² – 2 )? %3D а. 0 b. 1 с. -1 d. 2

A:

Q: The line integral P F.d7 can be evaluated using Stoke's Theorem where F = (2x, -3, 1) and C is an…

A:

Q: E Use Green's Theorem to evaluate the line integral along the given positively oriented curve. [ 4³…

A:

Q: 4. Let C be the unit circle in the xy-plane, and S be the boundary of the square with side 1,…

A:

Q: = Jó 7xds where C consists of the arc C₁ of the parabola y 3x² from (0,0) to Compute the integral I…

A:

Q: (1,0) C is the path from (1, v2) to (1, 0) along line segments as shown in the figure above. Then…

A: The application of line integral is, it represents the work done by a vector function acting along a…

Q: Sc 7ydx + 3z dy where C is the straight line path from (2, 4) to (4, 7).

A: The parametric equation of the straight line between the points (a,b), (c,d) is x-ac-a=y-bd-b=t,…

Q: Prove that the following curves have infinitely many rational points: y? = a3 – 3x? + 3x – 1, y? =…

A: The given curve is y2=x3-3x2+3x-1. Rewrite this as follows. y2=x3-3x2+3x-1y2=x-13y=x-13         or…

Q: 3. Evaluate the line integral (3ry² + 6y) da, where C' is the path traced by first moving from the…

A: The given problem is to evaluate the given line integral of (3xy2+6y) over the given path C which is…

Q: Use Green's Theorem to evaluate the line integral fe4y² dx + 3x² dy, where C is the boundary of the…

A: Let us solve above problem by using the Green's theorem.

Q: 2. Evaluate (x + y) dA, D is bounded by y = √æ and y = x².

A: The given integral is Where D is bounded by

Q: 1. Find the area of the region bounded by the ves y = x³ – 5x + 6, y = 10 – 4x – 4x2 and the line x…

A:

Q: Which of the following is/are points on the curve y-x Br+ 22x - 24x +9 whore the tangent line is…

A: We need to find the points on the curve where the tangent line is parallel to the x-axis.

Q: where Dx = X₁-X₂ and Dy = |Y₁ — Y2]. Assume that the two locations are independent and uniformly…

A:

Q: (47) Let C be the curve y = 5x where 1 ≤x≤9. Calculate the length of C.

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Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: Consider f (x, y) 3x² + xy + 3y². Use calculus to find the extreme values of fon the circle x² + y²…

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Q: - Let f(x, y) = x² + y²-4 and let C be the circle x² + y² = 9 traced once counterclockwise. Evaluate…

A:

Q: 4. Find all local extremum of the functionf (x,y) = x2 – y2 bounded by the circle x2 + y2 = 1: %3D

A:

Q: Compute the length of the curve r(t) = (-4t, 5t — 3, -2t + 3) over the interval 0 ≤ t ≤9 L =

A:

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: 23. Let w x₁ + iy₁ and 2 = x₂ + y₂. (a) Show that the distance WZ between the points w and z is |z −…

A:

Q: Evaluate the line integral x²z ds, where C is the line segment from (0,6, 2) to (8, 5, 1).

A:

Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

A:

Q: Evaluate the line integral where C is the curve made up of the straight line segments from the…

A: We will find parametric equations of line segment and then find line integral