5. Consider the line integral Jy dx- dx + 2x dy and the three different curves (a) C₁: (1+t,1+3t) with 0≤t≤1, (b) C₂: (t, t²) with 1 ≤ t ≤ 2, (c) C3: (t, 1) for 1 ≤ t ≤ 2 and (2, t) for 1 ≤ t ≤ 4.

Q: Find the length of the curve r(t) =〈2/5t^5/2−2/3t^3/2, t^2, 1/2t^2+t+ 7〉for 0≤t≤3.

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Q: Where are the relative extrema (local maximum and minimum) on the curve? y = 3x² – x A. (0, 0) only…

A: given curve is y=3x2-x3 find the local maxima and local minima

Q: (1 point) Evaluate the line integral y dx + x dy where C is the parameterized path x 1 x = t², y =…

A:

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: b) Evaluate S(2y + 4z)dx + (2æ + 3z)dy + (4x + 3y)dz, where C is the curve given by r(t) = for 0 <t…

A: given ∫C2y+4zdx+2x+3zdy+4x+3ydz where C is the curve given by rt=t3,2sinπt2,3cosπt2 for 0≤t≤1…

Q: (5xy --- 6x(2^

A: Given,        F=(5xy-6x2)i+(2y-4x)j and   y=x3 from the point (1, 1) to (2, 8).

Q: Question 2 Find the minimum value of (x.y)=2xr+4y on the curve x^2+xy+y^2=16 Select one: а. -18 C b.…

A: Given, fx,y=2x+4yx2+xy+y2=16         let gx, ygx,y=x2+xy+y2-16

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: f(x,y) be defined implicitly as a function of x and y by the 3xyz =exyz Əz Əz yay ax Əz Əz Find and…

A:

Q: y=f(x)=x' - 4x +10 find the interval that f(x) graph is concave down. O A) (2, infinite) O B) (0, 3)…

A: Given that the function y=f(x)=x4-4x3+10 Find the interval such that graph of the given function is…

Q: Compute F · dr where F(x, y) = and C is the path traced by the line segment starting at (0, −1) and…

A:

Q: 11- Find the moment of inertia about x-axis bounded by the curve y = 6- x² and the line y = x + 1

A: The given information in the question is the curve y=6-x2 and the line y = x + 1. The objective is…

Q: Let be a curve in the xy-plane. Find d'y dx² -|(x, y)=(1, 1) = _ 6x³3 + 19y³ = 25 તે પુ da²(x,…

A:

Q: Find the Frenet apparatus of the curve α(t)=(t , (t^2)/2 , (t^3)/6 )

A: Given α(t)=(t,t22,t36)

Q: =

A:

Q: 3) Evaluate f.(y + z)dx + (x + z)dy + (x + y)dz, C consists of line segments from (0,0,0) to…

A:

Q: The path C is a line segment of length 13 in the plane starting at (2, 2). For f(x, y) = 5x + 12y,…

A:

Q: Evaluate ∮C (x + 3y)dx + ydy where C is the Jordan curve given by the graphs of y = e^x, y = e^−x…

A: ∮Cx+3ydx+ydy Where C:y=ex, y=e-x, y=e-1

Q: F. dr where F = yzi + xzj +xyk and C is the curve x = t, y = 2t², z = –2t² with 0<t < 1.

A: Given F=yzi+xzj+xyk and r=ti+2t2j-2t2k Now the vector field along the curve can be given by…

Q: Find ((x2 + 4y)i + 3 y j) · dř where C consists of the three line segments from (1,0,0) to (1,4, 0)…

A:

Q: 1 (vz,xz,xy) dr where C is the union of the curve y=x* from (0,0,0) to 1+xyz Evaluate (11,0) and the…

A: