III 6(x3 + xy²) dv, where E is the solid in the first octant that lies beneath the paraboloid z = 4 4 - x2 - y2.

Q: 1. The solid that is above by the paraboloids z = 2- x² – y² and below by the paraboloids z = x? +…

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Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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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: Evaluate the triple integral ∫∫∫T (x^2) dV where T is the tetrahedron with vertices (0, 0, 0), (1,…

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Q: 1. a) Use the cylindrical coordinates to evaluate (3 + xy)dV, where E is the solid E in the first…

A: Here is the solution of the given problem.

Q: Find the Wronskian W[y,, y,, yal where Y1=t+ 10, y2= sin(2 f), y3 = cos(2 t). a. 8 t+88 b. -8-t-80

A: Given: y1=t+10 ,y2=sin2t ,y3=cos2t

Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: d?T - 0.15T = 0 dx2 btain a solution for a 10-m rod with I(0) = 240 and T(10) = 150: a) Analytically…

A: Given,       d2Tdx2-0.15T=0,    T(0)=240  and T(10)=150

Q: -8 6. Evaluate the integral +y² dydx

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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: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: 14) The solid is generated by rotating R about y = -3. 15) The solid is generated by rotating R…

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Q: Find the antiderivative of…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: 5. Use the separation of variables method to determine the solution u(x; t) of the heat transfer…

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Q: 2 Find.all.se.cond.partial.devevatives:. f(x,y)In(3xi+5.y..b.ue sint C.Z-ytan x a..

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Q: Find the general solution of ху — у 3D 2x In(х). а) Оу%3D х In(x) + Сх b) Oy = x(In(x))² + Cx с) Оу…

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Q: Evaluate the triple integral // x dV, where T is the solid tetrahedron with vertices T (0,0, 0),…

A: Here we have to evaluate the triple integral , where T is the solid tetrahedron with vertices…

Q: 10. Let D be the solid inside the cylinder r= cos , above the xy-plane and under the paraboloid…

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Q: H.W: Evaluate the integral 3. -4y)dydx x*ydxdy 1 -1

A: ∫xndx=xn+1n+1

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: 8) Consider the solid Q that is generated in the first octant by the surfaces S₁: (x - 2)² + (y-2)²…

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Q: 1. Use the cylindrical coordinate to evaluate ff. x² + y²dV _where G is the solid bounded by…

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Q: The equation 2x²y" +3xy'-(1+x)y =o has a regular singular point at x,= o %3D

A: The differential equation of the form, a(x)y''+b(x)y'+c(x)y=0 has a regular singular point at x=x0 ,…

Q: 11. The y-coordinate of the centroid of the solid in part IV is.. A. 0 В. 1 С. 2 D. 3

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Q: x =0 is a regular singular point of the DE: xy" + In|x|y' +3xy =0

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Q: 1 August - 7 August / rty The integral (2x +y+1) dz dy da is: 0. 0, Select one: None of these 11 84…

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Q: Evaluate the triple integral II. x* dV, where T' is the solid tetrahedron h vertices (0, 0, 0),…

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Q: Evaluate 1 dv √x² + G where G is a solid that lies inside the cylinder x² + (y − 2)² = 4, above the…

A: Please see the attachment

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: 27) If the solid of revolution formed by rotating R2 about the y-axis is a cylindrical shell, then…

A: You have posted multiple questions. As per the instruction, we will be answering only the first one…

Q: 4. Aşağıdaki denklemi y(2)=1 başlangıç koşulu için çözünüz dy (x² + 1 ) + 4xy = x dx

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Q: No. Date Evaluate fff dv G x² + y² where G is a solid that lies inside cylinder *+(4-2)² =4 obove…

A: we will use cylindrical co ordinate system to solve the given integral

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: A spherical snowball of volume V cm³ and radius r cm dr = -5 cm/s. dt melts in such a way that -…

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Q: t Consider the DE 'y" - zy' - 8y = 3z - A) Verify that y =and y =z satisfy the DE: z'y" - zy -8y =…

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Q: 6. The electric potential at each point (x.y) in the region R: 120.ys1 is given by V=…

A: The electic potential function is given by: V=48xy-32x3-24y2 To locate the maximum and minimum of it…

Q: 1 1-) ху Q3. Evaluate the double integral dxdy /1 – y², 0. 0. |

A: Double integration

Q: =+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the…

A: See the details solution in below

Q: (b) Find the surface area of the portion of the paraboloid z-2-x -y above the xy- plane. AMINATION A…

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Q: 15. Use the indicated change of variables to evaluate the double integral ||18xy dA where R is the…

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Q: 8. Evaluate x dV where E is the solid enclosed by the paraboloid r = y²+2? and the plane x = 9

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Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

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Q: 4. Evaluate x²dV G where G is a solid that lies in the first octant bounded by x? + y? = 3z and z =…

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Q: 3 Find the bounded Solution of : = xt メ>。,t>。 >y(メノ) where y cx, o) = %3D and y co,t) = 0 . Ansi] y=…

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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: ³ SS ²0 Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (3,0,0), (0,6,0), an

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Q: Consider the solid Q shown in the following figure 2.x + 3y + 3z = 6 S y? + x = 2 2 If S: 2x + 3y +…

A: The given surface is as follows: 2x+3y+3z=63z=6-2x-3yz=136-2x-3yz=2-23x-y The projection of the…

Q: Let (x² – x)ʻy" +y' -y=0,the D.E has regular singular point at x =

A: The DE x2-x2y''+y'-y=0. Then we have to find the regular singular points for the given DE.