Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0

Q: Let f(x, y,z) = x² sin y +y e, where x t +3,y = net-1 and z = In 2t. %3D at t = 1 is: dt O -12n O…

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Q: Solve the triple integral I| (x² + y² + z²)7/2 dV where B is the unit ball B O 2n 2л О Зл 5 o 7n 5 O…

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Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: (a) Find an antiderivative of x/16 - x*. 1 4 (b) Compute the integral x'V 16– x* dx. |

A: Explanation of the solution is given below...

Q: 1. Evaluate the integral: I = 2x drdydz where the solid S is defined as: S = {(r, y, z) E R³:x > 0;…

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Q: Locate the singular point for the o.d.e (x3 + x2) y'' + (x2 – 2x) y' + 4y = 0 and classify them.

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Q: Find all local extrema of the Dirichlet function, defined on (0, 1) by 0, if x is irrational if r =…

A: A function can infinite number of local maxima's and local minima's but there would always be one…

Q: t°et dt 8-11. Evaluate the following integrals: (a) / (d) / s2'd 4x 3xet dx x In(x) dx (Vz) dz x³e-…

A: solution: the objective is to find the integral

Q: -JIL e √x² + y² dv, where E is the region that lies inside the cylinder x² + y² = 4 and between the…

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: -2-3 Evaluate the integral o S Jy² 2y dx dy.

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Q: Q3)Verify the Greens theorem to the integral f(2x*y-x)dy +(2yx- y)dx where C is atriangle its…

A: Green's theorem

Q: 9. Evaluate the integral // V2 + y² + z² – 3 dV where S lies between a² + y² +2² = 1 and a? + y² +…

A: Given integral, ∭sx2+y2+z2-3dV Where S lies between x2+y2+z2=1 and x2+y2+z2=9. The spherical…

Q: Evaluate the integral ∫c(2x-y)dx+(x+7y)dy along the path C, defined as y=9-x2 from (0,9) to (3,0)

A: Given ∫c2x-ydx+x+7ydy  where y=9-x2  from 0,9 to 3,0 Parametrize C by xt,yt=t,9-t2 and 0≤t≤3

Q: Evaluate the integral S dx 2x3 - 3xx 1 -In 2/2 "I/3x + /2 +C En(2 { x³ - 3x x)+c 1 V2 + V3x -In + C…

A: First we take common x3/4 then put√x=t  And using integration of 1/a2 - x2

Q: The DE (xy - 4x') – x²y = 0 is dx Select one: O a. Homogeneous and Bernoulli. O b. Nonhomogenous and…

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Q: Find the general solution of the DE dyldx = y(x – y) /x^2. O y = C/ In(y) O y = C/ In(x) O y = x /…

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Q: Find the bounded solution of au Əx = 2 อน at + U_if_U(x, 0) = 6e-³x. 1

A: Given: The equation is ∂u∂x=2∂u∂t+u and the given initial condition is ux,0=6e-3x. To find: The…

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

A: We have to find solutions

Q: By using Green's Theorem, evaluate the integral (1+xy') dx +x²y dy, where R is the closed R path…

A: From the given problem:   I=∫R1+xy2dx+x2ydy   From Green's theorem:   ∫F1dx+F2dy=∬∂F2∂x-∂F1∂ydxdy…

Q: Evaluate the integral. S yz dx dz dy 0 2 2 O 128 3

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Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

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Q: Wyx %3D If w = e* + x In y + y In x prove that Wgy

A: Consider a multivariable function . Then the derivative of the function with respect to x is the…

Q: 2. Prove the following: i. Let c > 0. Then |x| <c -c <x<c. |x| 2 x, Vx E R. |x + yl < ]x[ + lyl vx,…

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Q: Evaluate the integral: 1. - 1 (1- 5x + x³ – 2x5 5х + x3 — 2x5 dx x2 2. S(y³ – 3,/y+ Vy) dy

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Q: y = In z I at x = 1: Oy=-x+1 Oy=-x-1 Oy=x-1 Oy=x+1

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: Evaluate the iterated integral. 2 3 4 (x² + y² + z² ) dx dy dz -2 0 0

A: ∫-22∫03∫04x2+y2+z2dxdydz

Q: 1) Consider (x, y, z) = 2xyz - x²y³ v(x, y, z) = xy² + y sin(z) F(x, y, z) = F₂(x, y, z)i + F₂(x, y,…

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Q: 3 Find the bounded Solution of o учу j²y аха = xt dt² sy( dy where y(x, 0) = and y (o₂t) = 0 (x,0)…

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Q: which of the following property is correct for J (x) d dx n-1 .a d (x" Jn (x))=x" Jn+1(x) dx .b d…

A: For Bessel function ddxxnJnx=xnJn-1x

Q: 4. Evaluate the integral f. x'y°dy – x5y'dx, where C is the square determined by the 0, y = 0, x =…

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Q: 1 Evaluate the double integral| dx dy where T is the quadrilateral bounded by the lines x = 1, x =…

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Q: a) a fonction f (xy) is homogeneous of degree 7 in X and y it and only it

A: As per bartleby guidelines we only give first question answers.

Q: #1. Evaluate the triple integral xy*av, xy?dV, B where B is given by B = {(x,y,z): 2 <x< 3, -1< y <…

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Q: H.W: Evaluate the integral: 1. √2 3y 8-x²-y² SS S 0 0 x²+3y² dzdxdy

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Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: Evaluate the integral. 고-36 x² – 36 . 6cos- (승) +0 /x² – 36 - dx = Vx² – 36 – 6cos¬! + C x² – 36…

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Q: 2. Let z = sin(xy) + x siny,x=u² + w² and y = uw. 2a. Compute Vz= when u = 0 and w = 1.

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Q: Verify Green's Theorem by evaluating both integrals ам √₁ y ² dx + x² dy = √₂√ √ (³x - dA ax ду for…

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Q: A:= {(x, y) € R² :1< log(x) < 2}. = {(x, y, z) E R³: sin(xy² + «/2) · cos(z) = 1} . (a) Decide…

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Q: Poblam cu (a) Compute Cm 2月-/ where xe [-,]. (1) 2n 2n-1 where ze C-1,1]. (b) Gompule Cm z nっ%

A: (a)

Q: O Evaluate the path integral between the points A = (1,3) and B = (2,5) of: (x²y + 2y)dy, with y =…

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Q: Solve the problem. dw Evaluate dv at (u, v) = (2, 2) for the function w(x, y) = xy 2 - In x; x = e…

A: We will find the dw/dv. at the point (u,v) = (2,2)

Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: dz for z = da z In(zy) + y, y = c os (x² + 1)

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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. Evaluate the triple integral SSS x²y°z=dV,where E is the rectangular box given by E=

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.