2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its value in the integration from A: (0, T, 1) to B: (1, , 1).

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Q: 4 sin 3y–6 dy cos 3y

A: We'll evaluate the integral as following.

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A: As per the question we are given a initial boundary value problem as : ut - 3uxx = 0 And we have to…

Q: •12 Evaluate the integral dx dy by reversing the 3 order of integration.

A: To evaluate: The integral of ∫012∫y34ex2dxdy by reversing the order. Explanation: Consider the image…

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Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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A: Here we have to verify the Green's theorem.

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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

A: If line Integral is path independent then there exist a function which is called potential function

Q: Set up an iterated triple integral equal to | = √√3 √3-x² √√30 x²+y² 3 √2-√4-x²-y² 2y dz dy dx…

A: The given problem is to set the given triple integral in Cartesian coordinates to convert into the…

Q: Evaluate the iterated triple integral II" -dx dz dy .

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Q: Set up an iterated triple integral equal to √√3 S√ SO 3-x² x²+y² 3 2- 4-x²-y² using: a. Cylindrical…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate fz² In z dz using integration by parts 2 Onz-+ +c Oz-+ Onz-+c Oz² Inz - 2 + c

A: ∫z2lnzdz=∫(lnz)z2dz=(lnz)z33-∫1zz33dz+c=(lnz)z33-∫z23dz+c=(lnz)z33-13z33+c=(lnz)z33-z39+c=z33(lnz)-z…

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Q: Pind the ualue of e is an integrating facko of ly-y')+xy'so

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let…

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A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

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Q: Evaluate triple integral ſ´, S,2 ¯* dz dx dy .

A: We can solve this as follows:

Q: Solve the equation by Cauchy's integral theorem. 1- dz 2- . 2z(4– z)dz

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…

Q: Find the solution in the form of Fourier integrals: U₁-3 = 0, uz (0, t) = 0, |u(x, t) bounded as…

A: We have the following partial differential equation : ut - 3uxx = 0  , x,t > 0 With boundary…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=0,…

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Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

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Q: 2. Evaluate O (2y + In(5x² +3)) dx + (10x 3) dy along the boundary of the elliptic- region 4. y? 1…

A: Introduction: Green's theorem is very efficient in calculating line integral. When the line intgeral…

Q: Set up UP the integrel the Pegioni Th bounded 2x2 and y =l+ x F(x,y) dA in by: y= 2x? 2. 4.

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=2,…

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Q: 3. Verify the result shown using 'integration by parts'. | t sin(nt) dt = – -t 1 t cos(nt) + 1…

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Q: In Exercises 19–22, state why it is difficult/impossible to in- tegrate the iterated integral in the…

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Q: v) ₁ √√¹-x² sin(x² + y²) dzdydx fő

A: Given is  ∫01∫01-x2∫01sinx2+y2dzdydx In order to solve this integral it is needed to first convert…

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A: For the given  Cos t = 1-t2+t24!-t36!+.... error is estimated as shown below

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A: Sol

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…

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Q: In 3 | (1-x)e"dx ах In

A: Consider the given integral

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Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…

Q: 2. Calculate where the curve described by the parametric pair x= St dt an of integration as…

A: Given: The parametric pair is, x = ∫ t . dt    ........( 1 )  and  y = ∫  t4 - 4 r3  dt   ......( 2…