that the in tegral is inde pen dent the path, and v6e S how the Fundamental to of of Line Integrals find its value Theorem I,4) 2uy° dn+ Iu²y² dy C21-2)

Q: Evaluate the line integral x¹ z ds, where C is the line segment from (0, 7, 5) to (7, 1, 2). C

A: We have to evaluate  where  is the line segment from  to

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

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Q: Find the equation of the tangent line to the curve 3 x' + 2 y – 22 = 3 xy – x at the point (2, 2).…

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Q: 2 question Jet flz)= (7-1)sinllx-1)²+2y2) for fl)=0 ond 3= x + iy e ¢\ {13. a) Show that the…

A: fz=z¯-1sin(x-1)2+2y2z-12f1=0 and z=x+iy∈ℂ\1To show that: f is continuous at point z0 =1 and f has no…

Q: QI/ Find the value of the line integral , F.dr when F-yi-xyj and C is the circular are in figure…

A:

Q: ²²-i)² dx 2³+dz when the contour C is the circle |z − 21 = 5 +4 1 Z- COSZ Cosz, dz when the contour…

A: According to the guidelines only three subparts should be answered. Therefore to answer the rest of…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Since the tangent equation of f(x) = x^3 – x^2 + 3x – 5 drawn from the x = 1 apse point on it is y =…

A: Given : Function  f(x) = x3 – x2 + 3x – 5 Tangent equation on the given function f(x) at point x =…

Q: consists of y = 4-x and straight line from (-2,0) to (2,0). Sketch the curve C. 64 ans: 3

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Q: Let C be the curve given by X- Sin/tr) and y=t, from ĭst 55. sin/tT and y=t, from ist E5. Find the…

A: According to Fundamental Theorem of Line Integral, the definite integral of a function is evaluated…

Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Find the equation of the tangent to y = e A) y=-x-1 OB) y = ex+1 C) y=x+1 O D) D) y = x + x at x =…

A: Find the equation of the tangent to y= esinx at x=0.

Q: Consider the line integral given by , y-dx+xdy Ca) Evaluate the line integral where Cis the /ne…

A: We will find out the required value.

Q: 17) Use question (5) and FTC for Line Integrals to ev aluate the line integral If Cis the circle…

A: Fundamental theorem of calculus for line integral : Suppose that C is a smooth curve given by rt→ ,…

Q: 0.8 0.6 0.4 0.2 of -0.2 -0.4 -0.6 0.5 1.5 2 5 A direction field for y'= -(2xy2 + y³) 2.5

A: Given differential equation is: y'=-2xy2+y3. We have to sketch the direction field for the given…

Q: The line integral 2xe" dæ + a²e" dy + (1 – 2²)e¬²² dz is not independent of path.

A: The line integral ∫CF·dr is independent of path if the curl of F is zero, that is, ∇×F=0. Here, The…

Q: ® Use Craumoy's rule to solre fhe following linear syslems: rele to solve al fxy=0 8? S x+2y-2 = 0…

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Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = xz siny-√3 At point (1,1,2).…

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Q: Jse Green's Theorem to evaluate the line integral along the positively oriented closed curve C.…

A: The equation of a straight line joining two points x1, y1 and x2, y2 is given by the formula: y-y1 =…

Q: Question# 4 f(x)=x² for 0<x<2. Set up the integral that gives the arclength of the curve V1+x²dx L =…

A:

Q: Evaluate the integral c (xy+z^2)ds where c is the arc of the helix x=cos t ,y =sin t, z=t which…

A: To evaluate: The integral ∫c (xy+z2) ds where C is the arc of the helix x=cos t, y = sin t, z = t…

Q: F(x, y) = (x√x+y, a² + √y) and C is the circle x² + y² = 4 oriented counterclockwise What process…

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Q: Consider the function f( + ty)- 3z²y+i ain z nw that thin funeticon does not satisfy the…

A: a) The given function is: fx+iy=3x2y+isin x Cauchy Riemann equation:  Let fz=u+iv be a complex…

Q: for the curve F= [4x³,0,0] consider the below curves extended together from-2 to 1. Evaluate the…

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Q: Previous Problem List Next ‚ Let F = (6x²y + 2y³ + 7e²)i + (5ex² +54x) j. Consider the line integral…

A: Given, and consider the line integral of  around the circle of radius , centered at the origin and…

Q: show that uuX)-X (1+x*J% I'sasolutionto integralequation ux)=X-sinh (x-t)u (t) dt

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Q: let a>o be a fixed real number. Let acoscx?3+ X ln cy) = y2+2xy+ & -1 find the equation of the…

A: the given equation of the curve is: a2cosx2+xlny=y2+2xy+a2-1 we have to find the equation of the…