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 fc (2 + x*y)s, where C is the half circle x + y? = 1 in the upper half…

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Q: F(x, y) = (2x - y, x + 3y), and let C be the path along the parabola y = 2x² from (0, 0) to (2,8).…

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Q: 7. Set up the integral in polar form that gives the area of the surface formed by revolving the…

A: We have to set up the integral in polar form such that the area of the surface formed by revolving…

Q: 2. (a) Use Pythagoras' theorem to find the length of the line segment y = 2x from (1, 2) to (2, 4).…

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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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: Let C be the curve which is the union of two line segments, the first going from (0,0) to (1, 1) and…

A: Our objective is given below:

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: If the curve C is the top semicircle x? + y? = 9 from (3, 0) to (-3, 0), evaluate the line integral…

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Q: v(e -Y cos x) • dr, where C is the line from (0,0) to (2x, kn 7)

A: The fundamental theorem of line integral, also known as gradient theorem states that suppose a curve…

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: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

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Q: Consider the parametric curve C that is defined by C: x=t^3, y=t^2+t, −1≤t≤3. c) Find a single…

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

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Q: x ds, where C is the portion of the parabola from (0,0) to (1, 1), followed by the line segment from…

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