Finel a formal solhon to the inital- boundary valve problem. Ugla, t) =6 uxx (x;t) , oexo ulx,0) = , o

Q: 4/ Find the area of the region enclosed between the curves y= cos 2x, y=0, x=TT/4, x= TT/2 ? ans/…

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Q: 46.) (a) Parameterize S the 1st octant portion of the cylinder y² + z² = 9, 0 <x<4 (b) Use above to…

A: y2+z2  0≤x≤4x=uy=3 cos vz=3 sin vparameterise the surface ass(u,v)=(u   3 cos v   3 sin v)0≤u≤4,…

Q: 5. Evaluate the integral xdx+ (x+y)dy where C is the curve x 1+y from (2,1) to (2,-1).

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Q: [-4ycos(x)+4sin(x)cos(x) +sec°(x)]dx +[4y=4sin(x)]dy = 0, y= TC = 0 2y-4ysin(x)-cos(2x)+ tan(x)= 1…

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Q: Evaluate the integral. 3 4x A y cos z dx dy dz 0 0 0 3 4x A I ly cos z dx dy dz = U 0 0 0 (Type an…

A: We have to find

Q: 1. Under the paraboloid = 3z2 + y? and above the region bounded by y = x and r= y² – y

A: Find point of intersection of:  y=xx=y2-y y=y2-yy2-2y=0y=0,2

Q: Solve the boundary value problem described by PDE: u„ - c?u = 0, OSxS1,120 BCs: u(0, t) =u (1, t)=…

A: The general solution for the homogeneous wave equation satisfying…

Q: 4. (a) Evaluate the integral (b) Show that 0 1 S [ f*cos(y²) dy da 0 Ste 1 + ex+y dx dy 4.

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Q: 2 Let f (x) = x on [0, 1] Calculate x dx and x dx by dissecting O, I] oaual narts and hence show…

A: Given

Q: -x), with respect to OY. 4. The area bounded by the curve 2x+2x -y -2 0 and the line y=2x with…

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Q: . 3. Compute E y 2 z 2 dV , where E is the region bounded by x  1
y 2
z 2 and x 

A: The given curves are

Q: What is the integrating factor of (1 + cos z) y' = sin z (sin z + sin rcoSI y) - CSC I sin z O1 +…

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Q: The surface area of the surface generated by revolving y= 1 – x² for 0<x<1 about the x – axis is s=…

A: The solution is as follows

Q: 3. E bölgesi y =| x ve y = 4 doğruları tarafından sınırlandırılan bölge olmak üzere | eu" sin(x³) dA…

A: Please see the explanation below....

Q: 1. Evaluate the triple integral // defined by the inequalities 0 <r < T, 0<yS1,0< z <7/6. xy sin…

A: From the given problem: ∫∫∫xysinyzdV Regions are: 0≤x≤π ; 0≤y≤1 ; 0≤z≤π6   So, we can write as:…

Q: Ive the following PDE with nonhomogeneous boundaries: PDE UttUxx = 0, BCs u(0, t) = sin(t), u(L, t)…

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Q: Evaluate the triple integral. -{x, v. 2) 1 0 s x s 1,0 s ys x, x szs 2x} 19yz cos(16x5) dV, where E…

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

Q: Let z = xy + x/x+y and a cos t, y = sin t. Then dz evaluated at dt is: Select one: O 0 V3-1 1-V3…

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Q: 17. Evaluate the line integral xe" dx +y sin yªdy along the triangular path consisting of the line…

A: Consider the given integral. I=∫Cxex2dx+ysiny2dy The given points are 0,0,2,3,1,0,0,0. Now, draw all…

Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: Integrate fcx)9,2) =X+y -Z over thep Poth from OLo.0.0) to A (2,1,2) given by, ostsi (C) = r z i…

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Q: 8. Depending on the real parameter p and q, what can you say about the result of the following im-…

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Q: Calculate the iterated integral. 1/2 (y + y2 cos(x)) dx dy

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Q: 0; x 0

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Q: 1. Evaluate the triple integral / / L xy sin (yz) dV; G is the rectangular box defined by the…

A: To evaluate the integral ∫∫∫GxysinyzdV where G is rectangular box defined by  0≤x≤π, 0≤y≤1, 0≤z≤π6.

Q: ÖRNEK : Ssin's sinº x cosx dx integralini hesaplayınız.

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Q: 2) Let 1 = f* cos y3 dydx. By reversing the order of integration of I, we get a. 1 = ²₂x cos y³ dx…

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Q: 11 Calculatk the line integral , f (x,y)ds for the given junc rion and path xiyl=xy Ht)= for 0st<4…

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Q: ди Әх and initial condition ди + + u = 0, x > 0, t > 0, Ət olve u(0,t) = 0 t > 0, and u(x,0) =…

A: Given That : ∂u∂x+∂u∂t+u=0 ,x&gt;0,t&gt;0u(0,t)=0 ,u(x,0)=sinx To Find : Solution of the Partial…

Q: Q5 Use Green's theorem to evaluate the line integral (cos.x+2y)dx+(x – sin y)dy C where C is the…

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Q: 1. Find of/ar, af/ay and of/0z (y- sin(x))² f(x, y) = (r - 1) (y+ 2) + S(1, y) = in(V + y²) + (z² +…

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Q: Eraluate: 1. JJR e-(n^²+yv) the eincles of padii 1& 2 dady, R is the region of between.

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

Q: Evaluate the triple integral. xy sin(yz) dV, where G is the rectangular box defined by the…

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Q: 2. Find the temperature distribution inside a solid parallelepiped with sides (a, b, c) whose faces…

A: Here, uxx + uyy +uzz = 0                                  .......1 with conditions, ux,y,z,0 = A…

Q: Q#03:Use Green's theorem to evaluate the line integral x³y² dx+ (cos5x – 2e2*y³)dy, where C is the…

A: According to the given information, it is required to evaluate the line integral using Green’s…

Q: O Sdlve the heaf flow problem ulo,tl = ul1, t) = 0, t>o u(x,oj= sin (2x) – 5 sin(6x) + 7sin (7x)

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Q: 1. x = t, y = 1/(1 +²), z = t² 2. x = cos 4t, y = t, z = sin 4t 3. x = t? – 2, y = t³, z = tª + 1 4.…

A: If any point (x,y,z) on the curve of a function can be represented in terms of a parameter t , then…

Q: 10- y(x + y + 1)dx + (x + 2)dy = 0 denklemi **1 + y' = 0 denklemine denktir. Bu son denklem için M,…

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Q: j ula,0) =f(2) solue (4 Us ing neumann Boundary Conditions o lg Periodic Boundary conditio, usile

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Q: 11 Let I= [[5 sin(v')cydx . By reversing the order of integration of I, we get:

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Q: Evaluate the double integral I2 = || y'dzdy T where T is a triangle with vertices (-4, 0), (0, 1),…

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Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: 4. Evaluate x² dV G where G is a solid that lies in the first octant bounded by x2 + y? = 3z and z =…

A: We have solid G in the first quadrant bounded by x2+y2=3z and z=3 equating the above two equations…

Q: Evaluate the line integral (4х + 5у)dx + (За — 6у)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: aluate the iterated double integral. 1 cos(y) /5 + cos² (y) dydx Saresin (2)

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Q: 1. Use a change of variables to evaluate [[ y- dA where R is the trapezoid with vertices (1,0,…

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Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: 8. Evaluate the line integral (x'dx+ xe"dy where C is the closed path along the triangle in the…

A: Here we have to evaluate the integral ∫cx2dx+xe-ydy where C is the closed path along the triangle in…

Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

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Q: Apply Green’s Theorem to evaluate the integrals ∮(3y dx + 2x dy)C: The boundary of 0≤ x ≤π, 0 ≤ y ≤…

A: According to Green's theorem - ∮Pdx+Qdy = ∬D dQdx-dPdydxdy          ...............(1)Given integral…