Let U(x,t), {x|0≤x≤π} be a vertically placed wire of length π with x position, t time, wave equation with k constant  (d^2U)/(dx^2)= 1/k(d^2U)/(dt^2)  It is written as .  For boundary conditions t≥0  U(0,t)=U(π,t)=0  Find U(x,t) using the separation method with the initial condition U(x,0) = 0

Q: 8. The region of integration D is bounded by the lines y = x,x + y ==,y = 0. Show that 1 | sin(x +…

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Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: State the area of the region, determined by the lines, y = 14x, y = 4x + 2, y = 14x – 4, y = 4x + 7…

A: we know we will use jacobian to transform the change of variables here .

Q: Evaluate triple integration of xz *dv with respect to E where E is the solid tetrahedron with…

A: Consider the provided question,

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

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Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

Q: The region bounded by x = 1 - y¹, x = 0 is rotate about the line y = -5. The volume of the resulting…

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

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Q: Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant

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Q: Find the center of mass of a thin plate of density δ = 3 bounded by the lines x = 0, y = x, and the…

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Q: 3 - Find the bounded ly y=2x-2, x=-1, x= 2 3 area y=2X - 2, x=-I, x= 2 4- Find the anea bondol .

A: Integrate the given parabola from x=-1 to x=2

Q: the volume of a solid bounded by x² + y² = 4,z=1,z = 9-3x-2y using triple integration.

A: We know that the to find the volume of a region by the triple integration V=∫∫∫dv   Where dv=dxdydz

Q: 5.) Find the volume of the solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate…

A: Above question is solved.

Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: 4. Illustrate and find the center of mass and moment of inertia with respect to x and y for the…

A: y = f(x) =4-x2   only in First quadrant…

Q: A solid is formed by revolving about the y-axis, the area bounded by the curve x^3=y, the y-axis,…

A: Solution :-

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

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Q: İki noktalı Gauss kareleme yöntemini kullanarak S dx integraline 1+16x4 yaklaşık değer bulunuz. 2…

A: we have given by integral ∫-12128x21+16x4dx we have to solve the integral by using two-point…

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: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

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

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Q: The short-time moving average of a process {X(t)} is defined as Y(t) X(s)ds. Prove that X(t) and…

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Q: The volume of the solid obtained by rotating the region bounded by y=(x^2), y=3x  about the line y=9…

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Q: 1 Find moment inertia of the halfdisk with mass density 8(x, y) = a. About the x axis b. About the…

A: We will find out the required value.

Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: The triangular region Ω has vertices (1, 1), (2, 0), and (2, 3).

A: My=∫12∫-x+22x-1kx2dydx

Q: Sketch the region R of integration and switch the order of integration. 81-x2 LV²²- -10 O -10 f(x,…

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Q: Let R be the region bounded by the parabola y = x 2 − 1 and the line y = x+ 1 and let f(x, y) = xy…

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Q: Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0)  and then to the…

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Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

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Q: Find the area of the region between the curve y = 3 - x2 and the line y = -1 by integrating with…

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Q: Evaluate the triple integral. 7x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: Here, E is the surface boiunded by the  paraboloid x=5y2+5z2 and the plane x=5. Now, at x=5,…

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

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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 line integral $ x*dx + xydx where C is the triangle with vertices at (0, 0), (0, 6) and…

A: Given Line Integral is ∮x4dx+xydy , where C is a triangle with vertices at (0,0), (0,6) and (6,0)…

Q: Consider the boundary value problém, azu a?u = 0, 0<x< 3, 0 < y < 3, %3D u(0, y) = 0, u(1,y) =3, 0 <…

A: Given :-  The boundary value problem , ∂2u∂x2 + ∂2u∂y2 =0  , 0&lt;x&lt;3  , 0&lt;y&lt;3  u0,y =0 ,…

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

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Q: A thin wire is bent into the shape of a line segment from (1, 2) to (−1, 1), and the curve y = x2…

A: Given: The thin wire with shape as line segment from 1,2 to -1,1 and along the curve y=x2 from -1,1…

Q: Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve…

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Q: 4 Set upinbegrl for th volume caboud x- -I y. 12 and

A: Volume problem.....

Q: 2. The solid bounded by y = 0, x = y², x = 4, and z = Octant (ie. x, Y, z > 0). 2x in the First

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: We have to compute the value of constant (C) by solving the given DE using the integrable…

Q: y =-x +4x + 2, y=x+2

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Q: A lamina is bounded by y-e and the lines y-0,r-0, and zI with density (r,y) - y. Find the moment of…

A: Calculate moment of inertia about y-axis:

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

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Q: 10. The solid bounded by y = 4, y – x = 1, z = x², and z = = 4.

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

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Q: Let I = Lr+ 3)dzdrde. Then the region of integration is presented in

A: We have to find which of the given figure is the region of integration.

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…