4. Which would not be sufficient to prove AWXZ AWYX? C ZWXZ = LY WZ А WX XW YW WZ D WX WX XY XZ WX %3D WZ ZX XY WY ARC at tho right

Q: 4. Evaluate: S. yx?dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t2 , (0 st< 1).

A:

Q: (a) Consider the following line integral L(adar + ydy + (az – y)dz) along a curve C given by r =…

A: Given integral    ∫Cx dx +y dy +xz-ydz

Q: SupposeThat w=XYz+XY +Z+3andx=3cost, %3D Y=35int, z=27, Evaluete dwl dtt= I 2

A: solution.

Q: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

Q: Evaluate the line integral / (7x + 3y)dx + (2x – 8y)dy along the curve C: x = 8 cos t, y = 16 sin t…

A:

Q: If u=x2y+y2z+z2x then show that du/dx + du/dy + du/dz = (x+y+z)2

A: Given u=x2y+y2z+z2x. Find dudx as follows.…

Q: Given z = 14 In(t) and y= 196 t then find dy %3D dx dy ||

A: Given a parametric equation:                                    x = f(t) , y = g(t)  the first…

Q: If y=xtan(x) then dy at x = Tt is: dx

A:

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Evaluate e*y dx dy by using trapezoidal and Simpson's rules.

A:

Q: Evaluate the line integral fe y dx + x dy where C is the parameterized path x = , y = f, 3 <iS9.…

A:

Q: Compute the irertia móment by x ( Ix=Sy?JA) tor number off segment n=s hyte multple-trapezoidal…

A:

Q: . Evaluate ſſ,G(r)dA where G(r, y, 2) = arctan(y/x) and S is given by z = x² + y², with z< 9, r 2 0,…

A: According to the given information, it is required to evaluate the integral.

Q: 31 Evalvate the line integral gy lx + 8z dy tx dz, r(t) = (2+ t +3 for Ja9ydxt8zdyt xdz =

A: The line integral ∫C9ydx+8zdy+xdz, r(t)=2+t-1,t3,t2 for 0≤t≤1. We have to evaluate this integral.

Q: Given YZ tangent to OJ at point Y, and mzWYZ = 104°, what is mW XY ? W mWXY

A:

Q: Show Z=arctan(y/x) satisfies Zxx+Zyy=0.

A:

Q: 45. If A = (y – 2x )1 + (3x + 2y)j, compute the circulation of A about a circle C in the xy plane…

A:

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A:

Q: Given that u = arctan(xyzw), calculate dyðw"

A:

Q: Evaluate       C(2x − y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32)

A: We have to evaluate the integral ∫2x-ydx+x+3ydy along the path C, where C:y=x52 from 0,0 to 4,32.

Q: Evaluate the line integral cy dx + x dy where C is the parameterized path x = y = t° , 2<t< 6. Scydx…

A:

Q: 5. Compute the arc length exactly y =x² -In x , 1 sx< 2

A: Given : y=14x2-12lnx , 1≤x≤2   To Find: Arc length

Q: Given YZ tangent to OJ at point Y, and mzWYX=104, what is mW XY? W

A:

Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: 1 Evaluate dV, where E lines between the spheres a2 +3? + 22 = 1 and E 22 + y2 + z2 = 9 in the first…

A: Solution

Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

A:

Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

A:

Q: From Rogawski ET 2e section 8.1, exercise 11. Approximate the arc length of the curve y = i x4 over…

A:

Q: Compute 2z dz (2² – i)3 when y is any arc z = z(t) in C with |z(t)| > 2 for every t, with…

A: Let the required arc be ABC, which starts at z=3 and ends at z=2i: The shaded area shows a sector…

Q: If C is any sectionally smooth curve, which of the following line integrals is NOT path-independent?…

A:

Q: O Evaluate tke lime iutegral. (x²+ Hy) ds where c 1s the lime segment from (9,o) te (1,3). (x²+ 42)…

A: Note- by company policy we solve only first 3 parts. Please ask remaining part as another question.…

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)'dy for Exact then My %3D

A:

Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: dw If w = f(x, y, z) = In(x² + y? z?),x = cost y = sin t ,z = 4VE , then is : dt %3D %3D

A:

Q: If (xcos(y) – y)dx + (xsin(y) + x)dy = 0 is not exact. %3D .A false .B True

A:

Q: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

A:

Q: if wa2ey-Inz find dw dt X=In (t*, 1) y=tant 2set

A: According to power rule of differentiation and according to product rule of differentiation . Also…

Q: Evaluate the line integral (2x + 4y)dx + (3x – 9y)dy along the curve C : æ = 2 cos t, y = 4 sin t (0…

A: We need to evaluate integral.

Q: d(xy) = ? tot al dofferentral ? Zryckt x dy=9 )totol pferibral?

A: Given

Q: Ex: verifay u = e* cos y is a solution of laplace eqution

A: Solution:Given             u=ex cos yTo verify u is a solution of Laplace equation:i.e.,…

Q: 1) The Arc Length of the curve f(x) = coshx, 0≤x≤ In3 is: d. 312 12 3 C. b. 2²/2 0.33 lorod by…

A:

Q: Al/ compute 6(4+ ec©*) dx + (siny + 3x?)dy cosx Where c is closed bounded region lying in the first…

A: Given (A) The given integral is ∮4+ecosxdx+siny+3x2dy and the region lies in between x2+y2=4 and…

Q: d the val 5) y= 2cos 30 6) y= 4sin 20 cos 0 7) cot F 7) y= sin (0-45) 8) y = 2 + cos 0 9) y= 3sin…

A:

Q: Show that the subtangent to y = x' at x = a is equal to a/3.

A: Definition used -                            Length of subtangent =ydxdy

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: If z=x+ iy=r(cos(0) + isin(@))then |z|=Vx²+y² =rO Z=r0 arc z=00

A: Given z=r(cos θ +i sin θ)   Modulus of complex number, |z|=x2+y2

Q: Evaluate the line integral [(5x + 7y)dz + (3x − 6y)dy along the curve C: x = 4 cost, y = 8 sin (0…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.