41 2 R' p 1 4-3-2-1 O 3 4 6, 5. 3.

Q: Let D. be the linear transformation fromc (a, 6] into cla, e). Find the preimage of the function.…

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Q: 1. What should be A for the path independent of (2,4) ry + A 2Ay – 1 dy y? dr+ (1,2) Moreover…

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Q: Compute the integral ∫dx / 5sinx+2cosx+2.

A: Apply t substitution

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Q: 43.) Show by checking cross partials that F = (4x³y² – 2xy³, 2x*y – 3x²y² + 4y³) is conservative Use…

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A: The objective of the question is evaluate the definite integral.

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Q: Let 1-ff Sysin(r' dvdy . By reversing the order of integration of 1,

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Q: 3dz 1. S 4-5z

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Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

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Q: Page 4of 8 3. Evaluate the following integral or show that it is divergent: roo In x xp a) S" x+1 b)…

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Q: use convoluHon Lapiace transform 15. to find Inverce (1+zs) =S

A: Let ft & gt be functions with Laplace transforms Fs & Gs respectively that is Lft=FS &…

Q: 4. Compute f'dr by using fundamental theorem of integral calculus.

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Q: Evaluate the double integral S ry° dydx

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you…

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: Prove that Cosh [m(t-x) Cosh mh 2mL 2mL

A: The given data is: To prove: emx1+e2mL+e-mx1+e-2mL=coshmL-xcoshmL

Q: Find the differential cquation a the (2.K) families af cirdes with center at and wi th radius r

A: To find: Differential equation of circle with centre 2,k and radius r. We know that equation of…

Q: and let ah -(-1'I Let In tan (a) for n = 0,1, 2 Intz 1) Show that In + Io+ り+! (-1)" for nal an-…

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Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: 1. What should be A for the path independent of (2,4) ry+ A dr+ (1,2) Moreover evaluate the integral…

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Q: 3. Compute the line integral of F(x, y) consisting of the line segment from (T,0) to (2, 5),…

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Q: Show that the following line integral is path independent (3,2) cosh (0,0) (8xdx+6ydy) 4.

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Q: Evaluate the following line integral. x-ds; C is line segment from (3,5,6) to (- 3,12,2).

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Q: 2 5 6z³ -8z¹+2z² 4 Z dz

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Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Step:-1 Note:- 1. ∫∇F.dr =∫fx i +fy j dx i +dy j  2. Fundamental Theorem of Calculus:- ∫bc F'(x) dx…

Q: 7. Use the Fundamental Theorem of Line Integrals to evaluate S(6xy, 3x² + 6y²) · dr where C is any…

A: Line integral theorem

Q: Compute the 1st and 2nd degree Taylor polynomials L(r, y) and Q(r, y) for f(1, y) = In(r +y?) at…

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Q: Evaluate the line integral S. 4x²ds, where C is the line segment from (-2, –1) to (0,–1) followed by…

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Q: Evaluate the double integral: dy dx 96 - - 32 - 32 96

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Q: A square is expanding in such a way that its diagonal is increasing at the rate of 2 in/s. (a) At…

A: GIven,  a square is expanding in such a way that its diagonal is increasing             at the rate…

Q: Find the Selution of (1-t +3t)4 (t) di - , (2) In which IL) denoter Bessel function

A: Leibniz integral rule : ddx∫bxaxFtdt=∫bxax∂∂xFtdt+Faxddxax-Fbxddxbx   Linear Volterra Equation of…

Q: Evaluate the integral. S- dx 8 =, x> 7 V49x2 - 64

A: Solution-

Q: Compute the path integral of F = ⟨ y , x ⟩ along the line segment starting at    ( 1 , 0 ) and…

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Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: Consider f dr. V1-16z² For the u-substitution u = 1 – 16x², which is the new integra 32 u2

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Q: It u-ys Int, Ya っ 3. to ny find by rusing ypropoiate chain rule

A: Given, Let, u=rs2ln(t), r=x2, s=4y+1, t=xy3

Q: 1. What should be A for the path independent of (2,4) ry +A -dr dy (1,2) Moreover evaluate the…

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Q: Show that the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – x + xp- y? fip- (1,2) Moreover…

A: According to the given information, it is required to find the value of  so that the below integral…

Q: dr 4 – z Integrate:

A: The given integral,∫54-x2dx

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: We have  I=∫(0,0)(3,5) cosh(x23+y25)(10xdx+6ydy)apply Green's…

Q: or state that it diverges. Show all work. Evaluate the given integral 5 dx 7. Jo x-3

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Q: continuous on ( UOUS O

A: Given function is: fx=3x+6a  ;  if x<-33ax-7b   ;   if-3≤x≤3x-12b   ;    if 3<x We have to…

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A: Given :∫-(9x2+7x)(x-1)(x+1)2dx

Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

A: