Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of path: fe %3D дд дх (12,16) – (28x³y³ dx + 35y*x*dy)

Q: Use Green Theorem to evaluate C P xydx+e'dy where Cis the path from (0,0) to (1,1) along the graph…

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Q: 5) Find the orthogonal trajectory of the family of curve given by y = In(r+b) %3D

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

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Q: Evaluate the integra ∮C -y3 dy + x3 dx for any closed path C.

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Q: 3. Show that the line integral + 2xy) dx + x² dy + 2xz dz, is independent of path in R3, where C…

A: We will find out the required value.

Q: Evaluate the line integral S 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). So…

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Q: 3. Show that the line integral 4. x + y)dx + dy C is independent of path and evaluate this integral…

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Q: Use the Trapezoidal Rule with n=6 to approximate π∫0sin2xdx.

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Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Find the exact sülution fur ylz Xtzy

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Q: Evaluate the integral ∫c(2x-y)dx+(x+7y)dy along the path C, defined as y=9-x2 from (0,9) to (3,0)

A: Given ∫c2x-ydx+x+7ydy  where y=9-x2  from 0,9 to 3,0 Parametrize C by xt,yt=t,9-t2 and 0≤t≤3

Q: find the Lineartransfromation T:Manz (R)R whose matrit Mp --

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Q: Find the total length of the loop of the curve 6y² = x(x – 2)² between x = 0 and x = 2. %3D

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Q: Show that the opelator Tilol defined by Y=19;)=Tx.-E] *=(h:)is Linear and bounded

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Q: Determine whether the work done along the path C is positive, negative, or zero. y O positive…

A: Consider that the sign of the work depend on the orientation of the path C. here the circulation can…

Q: Use Green Theorem to evaluate $ xydx+e'dy where C is the path from (0,0) to (1,1) along the graph of…

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Q: Find the equation of the normal line to the paraboloid z = 2x² +y² at the point (1,2,6). Select one:…

A: Equation of paraboloid  To find: The equation of normal at a point P = (1,2,6).

Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

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Q: Ue langrange multipliars to fined the Shortest distancé fam the to the pGine x+g+Z=1. point (7,0,)

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Find over xlapping area two equatione also gemetrical nepresentahon 2. 4'+v?=n, u?+cV- vn)=1 whore n…

A: Given curves are,…

Q: Find orthogoral trajectory to the family of dircles 3 x² + y? = 2Cy.

A: We have given equation of curve x2+y2=2Cy Then, differentiate both sides we get…

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: Solution is given below:

Q: Use Greens Theorem to evaluate: §. (2x + ev´)dy - (4y2 + e*")dx where C is the boundary of the…

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Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

Q: The scalar path integral 3(16-a y-) ds, where the path C is the straight line from the point (0,0)…

A: This is a problem of line integral. Since the path given for line integral is embedded on the x…

Q: Show that the line integral 22 +2ry) dx + x? dy + 2xz dz, is independent of path in R, where C runs…

A: We will find out the required values.

Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: The given equation of the cylinder us x2+y2=1 in the half space y≥0. Calculate the value of ∫∫∫xzdV,…

Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: 3y², Compute divà and curlà for à = (x²y²z?)î – (2xy² – 16x)ĵ + (9_)&.

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Q: D. Obtain the or thagonal trajectory of the family of ax+x =5+y3. aur ves of

A: Explanation of the answer is as follows

Q: about the line x = -2 ソ=2× ソ=2° 1 2

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Q: . By sketching the traces on the ry-, xz- and yz-plane

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Q: Evaluate p(10ey – 9x)dy – (yx – 5 In x)dx by using Green's Theorem where C is a trapezium with…

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Q: can u help me with pullbacks and integration plz

A: Given that the integral,

Q: Integrate h (x. y) = yi+xj over the indicated path: r(u) = ui+ u²j. ue [0, 1).

A: Given hx,y=yi+xj and ru=ui+u2j, u∈0,1 We have to integrate hx,y=yi+xj along the path ru=ui+u2j…

Q: Let X - Y (3, 0.02). Given Ttx = 300 calculated by the Esscher Premium Principl %3D

A: From the given information, X~γ3, 0.02 fx=0.023γ3e-0.02xx3-1, x&gt;0       =0.000004e-0.02xx2,…

Q: A straight-line fit y3 = e12), could be obtained with:

A:

Q: Evaluate the line integral §. xy²dx + 2x²y dy over triangular path with vertices (0,0), (2,2) and…

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Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

A: Introduction: Let P0=(x0,y0) is a point in the domain of f, and S is a surface defined by a…

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: dx Calculate for n = 6, using trapezoidal rule. %3D -11+ x²

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

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Q: Find the equations of the tanget plane and normal line to the graph of In(z2) x -= 3y³ – Vx at the…

A: Given graph is                                                        lnz2x-eyx=3y3-x Again…

Q: 5. Show that the following orthogonal families of curves: are x² + y² : = ax, x² + y? = by

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Q: THE DiffieRENITAL ECLATDOM WITH INITIAL conoirDON. dy- XSENX こ dx 3.2

A: Given query is to find the solution of the differential equation.

Q: Prove that the integral: √ [2xyz² dx + (x²z² + z cos yz)dy + (2x²yz + y cos yz)dz ] Is independent…

A: The given integral is ∫C2xyz2dx+x2z2+zcos yzdy+2x2yz+y cos yzdz. The objective is to prove that the…