Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the curve y = 2x – x² from (0,0) to (2,0) and the line segment from (2,0) to (0,0).

Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

A:

Q: Let f(æ)= / ve -1dt. -1 dt. Determine the arc length of y=f(x) from x=0 to x=2. Round your answer to…

A:

Q: Evaluate the line integral [(x+ y)dx+(x - y)dy, where C is the arc of the parabola y = 2x from (0,…

A: The integral in the form ∫CM(x,y)dx+N(x,y)dy involves the integration over a specific path C. In…

Q: Evaluate the line integral C: y² = 27x from (27, 27) to (0,0). NOTE: Enter the exact answer. 6-₂…

A:

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: 4. Evaluate the line integral 6. x²y dx – xy² dy where C consists of the arc of the circle 16 = x² +…

A: Given equation of circle is  x2+y2=16x2+y2=42 radius is 4 We have to calculate line integral ∮ cx2y…

Q: Use Green's Theorem to calculate line integral o sin(x²) dx + (3x – y) dy where C is a right…

A:

Q: If f=2yzj -zj+xk,evaluate line integral Fxdr along the curve x=cost,y=sint,z=2cost from t=0 to…

A:

Q: Evaluate the line integral F. dr where F = (3 sin x, 3 cos y, 10xz) and C is the path given by r(t)…

A:

Q: Use Green's Theorem to evaluate F. · dr, where F = (Va + 4y, 2x + and C consists of the arc of the…

A:

Q: Find the line integral with respect to arc length (5x + 3y)ds, where C is the line segment in the…

A: Given integral∫C5x+3ydswhere C is the line segment in x-y plane with the end points P(5,0) and…

Q: Evaluate the line integral, where C is the given curve. | xyz? ds, C is the line segment from (-2,…

A:

Q: Evaluate the line integral (direct method) | (3x– y) dx – x dy , where C consist of the parabola…

A:

Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

A:

Q: Use Green's Theorem to evaluate | F. dř, where F = (Va + 4y, 2x + 9) C consists of the arc of the…

A:

Q: Evaluate the line integral Fdr where F = 4.xyi – 8yj+ 3k and C is a curve given by y = 2x, z = 3…

A: Answer

Q: Evaluate the line integral (e*y+ 2x) dx + (e* + 1) dy, where C is a smooth curve from the point (0,…

A:

Q: Use Green's Theorem to evaluate F. dr, where F C consists of the arc of the curve y 1x x2 - from…

A:

Q: Use the theorem on saddle-node bifurcations from the lecture' to show that i = sin(r) sin(r) +…

A: Given dxdt=sinrsinx+cosx-er. Let us prove that 0,0 is the saddle-node bifurcation.   Theorem:…

Q: Evaluate the line integral C:y² = 30x from (30,30) to (0,0). NOTE: Enter the exact answer. [-ydr +…

A: line integral

Q: Evaluate the line integral F. dr, vhere F(z, y) = -yi-rj and C is the curve y = v4-a from (2,0) to…

A: We have to find the line integral

Q: Use a local linear approximation of the function f(z) = VI cos[(V2r)] at some approximate v3.98…

A: To use local linear approximation of the below function to approximate 3.98cos7.963π. fx=xcos2x3π

Q: | (xy dx + 2y dy)

A:

Q: Use Green's Theorem to evaluate dr, where F-(VE+ 4y, 2+ C consists of the arc of the curve y 1z - z…

A:

Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

A:

Q: Let f(x)= /Ve' – 1 dt . Determine the arc length of y=f(x) from =0 to =2. Round your answer to two…

A:

Q: Find arc length of vactor  valued function r(t)=ti+4tj+3tk over(0,1)

A: r(t)=ti+4tj+3tk over(0,1)

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A: Given line integral is,

Q: Find the Torsion along the curve: X = (t-sin t)ê +(1- cos t)ê, +tê,. %3D

A:

Q: | 5y? dx +xy dy

A:

Q: Set up an integral to compute the arc length L of the curve C: r(t) = (, 4t, v2t) %3D from the point…

A: I am going to setup an integral to compute the arc length of the given curve using the required…

Q: Show that UV=12 given, UX = 8, and XY = 10 using the intersecting %3D Secant-Tangent Theorem. * U

A:

Q: (a) Calculate the line integral (4x+2y²)dy where C' is the curve y = 2³, starting from z = 0, y = 0,…

A:

Q: Evaluate the line integral Jxy + z)ds where c the arc of circle x + y = 4, z= 0 from (2, 0, 0) to…

A:

Q: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

A:

Q: Evaluate the line integral -ydx + dy along the curve C: y = 30x from (30, 30) to (0,0). %3D NOTE:…

A:

Q: Evaluote the live integral | (xZ+ y) ds along the curve c defined byき)=くターも,スセt,-スモ> ON Osts I -21…

A:

Q: Evaluate the line integral, where C is the given curve. |(2y3 - Vx)dy, c is the arc of the curve y =…

A:

Q: Use Green's theorem to evaluate the line Integral for the curve C given in the figure. [2y dx + x…

A:

Q: Let curve C be the arc of x2 + y2 = 16 traversed once counterclockwise from (0, 4) to (0, -4). Let…

A:

Q: Use Green's Theorem to evaluate the line integral cos (y) dx + x²sin (y) dy along CoS the positively…

A:

Q: Evaluate the line integral ſp(xi + Vyi) · dr where D is the oriented curve shown below. (1,1) y = x2…

A: We know that r=xi+yj As, the path followed is y=x2 So, r=xi+x2j Let x=t, then  r=ti+t2jdrdt=i+2tj…

Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A:

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: Evaluate line integral F. dr, where F(x, y) =(2xy)i + (x²+3)j, and C is the path given by r(t) = t =…

A:

Q: The line integral (23 (x° + y°) ds, where C is the arc of the parabola y = x2 from (0,0) to (2, 4),…

A:

Q: Use Green's Theorem to evaluate F. dr, C where F = (Va + 6y, 4x + /ỹ C consists of the arc of the…

A: