Q2. Evalnate the double integral SS хе ク over the finite regieon 2 R={(x)): x2, y54ーx3

Q: Evaluate the integral. 1 dt t3 V2 -4

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Q: e In (xle ) (2– sec²x) sec(3A – x) sec³x dr What should be the value of A for to be integrable using…

A: integration by substitution method

Q: If | h(t)dt = 24 %3D and 8 |h(t)dt = 10.6 what does the following integral equal? h(t)dt- %3D

A: We know, ∫abf(x) dx = ∫acf(x) dx + ∫cbf(x) dx         (if a<c<b)

Q: Use symmetry to evaluate the double integral. 4xy 1+ x2 dA, R= {(x, Y) | -4 s x s 4,0 s y s 1}

A: When the upper and lower limits of definite integrals become same, the result is zero irrespective…

Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4- 3.…

A: Given:

Q: 13. Evaluate the triple integral: In y (z) dzdydx y2

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

Q: Evaluate the Integral dz 1. S z²+4z ANSWER: 1. - In + C 4 |z+4

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Q: Set up an integral for the length of y = Vx + 2, 2<x<7 using ds : |1+ () dx. %3D A. ds = S, 1+ 1 dx…

A: Solution:Given        y=x+2    2≤x≤7using ds=1+dydx2dxFormula:ddxxn=nxn-1

Q: Suppose that (z, y) = e-v and o(In 2, In 2) = 1. Please use the technique of %3D linear…

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Q: Suppose that f(x, y) = √√4² - x² - y² on the domain D = =4 Q Then the double integral of f(x, y)…

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Q: 70. Solid bounded above by x² + y² + z² = 36 and below by = 2 Vx + y?

A: Given: Consider The volume of any solid E in R3

Q: Evaluate the integrals in Exercises 7. (x² + y² + z²) dz dy dx 0 J0

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Q: Calculate the double integral. 3xy? dA, R = -{(x, m10 sx 5 3,-25 ys 2} -2 s ys2} .2 + 1

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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…

Q: Suppose that (x, y) = x+ 4y on the domain D = {(r, y) | 15x< 2, x? sys4. D Then the double integral…

A: Given that, f(x, y) = x + 4y and   {1≤x≤2},  {x2 ≤y≤4} We have to calculate the value of ∬Df(x, y)…

Q: 16. Let D-((, y, z):05zs2, 0≤ y ≤1, 05:5z+y). Find the triple integral: 72xy³ dv.

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Q: Suppose that f(r, y) = 2x + 4y at which {(x, y) |-1<a < 3, - 1<y< 3}. Then the double integral of…

A: ∫∫Df(x,y)dx dy=∫∫D2x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13∫-132x+4ydx dy=∫-13x2+4xy3-1…

Q: .3 Evaluate the integral LST wy+x*v+vz) dzdydx 0, 2.

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Q: W= Pcxiy,Z) = In (x+y+z) ,x= cost, 2. %3D 2X = Cost, y- Sint and z= 4VE >use chain rule to Rind dw…

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Q: Set up an integral for the length of y = vx + 2, 2 2 <x<7 using ds = 1+ ) dy. A. ds = f, /1+ 4y²dy…

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Q: ¡(z+1)dz 3 where C is z+2|= |z+2\=% z'-4z

A:

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: Use the transformation u = - -6x +y, to evaluate the integral [ ( (5x • y) dx dy, where R is the…

A: use the transform u=-6x+y, v=5x+ywe evaluate ∫∫R 5x+y dx dywhere R is the parallelogram bounded by…

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

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Q: Find the value of the line integral 6xy dx + (3x² + 4y2)dy, where C is an ellipse 16 + = 1 from (4,…

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Q: Evaluate the triple integral: 2 x (Iny (z) dzdydx

A: ∫12∫1x∫y2ln(y)zdzdydx=∫12∫1xz22y2ln(y)dydx=12∫12∫1xlny2-y4dydx Now,…

Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2,…

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: Let y = 5x + 4c +3. If Ar 0.1 at z 5, use linear approximation to estimate Ay

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Q: Calculate the double integral. 8x dA, R = [0, 8] × [0, 1] 1 + xy

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Q: Evaluate the triple integralE 7xdV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the plane…

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Q: Evaluate fff 12y - 8x dV wherein the limits of integration are the region behind y = 10-2z and in…

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Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

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Q: Evaluate the double integral. 8xy2 dA,    D is enclosed by x = 0 and x = (4-y^2)^1/2

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 7y2 + 7z² and the…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: Evaluate the triple integral. 8x dV, where E is bounded by the paraboloid x = 2y2 + 2z2 and the…

A: The objective is to evaluate the triple integral ∫∫∫E8xdV, where E is bounded by the paraboloid…

Q: Consider the indefinite integral " (5x³ + 4x² – 75x – 68 22 – 16 da Then the integrand decomposes…

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Q: #1. Evaluate (2x – 5y) dA, R where R is the parallelogram with vertices (0,0), (2,3), (–1,4) and…

A: The given region R is a parallelogram with vertices as shown in below graph. We have to use change…

Q: 7. Verify Green's Theorem for O (6+ x²) dx + (1 – 2xy) dy where C' is shown below by (a) computing…

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Q: Suppose that f (x, y) = 8x + 7y at which {(x, y) | – 2 < x < 3, – 2 < y < 3}. - D Then the double…

A: Use the integrating limit given on the set separately for x aand y

Q: Evaluate the triple integral. 10x dv, where E is bounded by the paraboloid x = 2y² + 2z2 and the…

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Q: Suppose that f(c, y): at which {(x, y) | 0 s< 1, - a <yS vE}. 1+ x Then the double integral of f(x,…

A: According to question given that f(x,y)=y1+x at which {x,y) |0≤x≤1, -x≤y≤x

Q: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 b. dz a. √21-23 = dz · Soz (²-2) 4…

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Q: Evaluate the integrally.dy.W 6y+ 34

A: To evaluate