W Q2.JPG x3+10 dx is ax + bln x -Arctan X-e The resulting integral of f + C, where a, b, d, e, and x3-2x²+5x f are integers. What is the value of b? A) -1 в) з D -5

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

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Q: we want to evaluate the following integral by sustitution; |xV4x+ldx-→u = 4x+1 fxV4x+ ldx =(u" -u"…

A: Here,                 ∫ x4x+1dxLet u=4x+1.=∫uu-116du=116·∫uu-1du=116·∫ u32-udu So, here n=3/2 and…

Q: Suppose that f(x, y) = √√4 - x² - y² at which {(x, y) | x² + y² ≤ 4}. tr=2 a Then the double…

A: Polar co-ordinate are given as x=rcosθy=rsinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

Q: Define freedholm, Volterra and Singular is a solution of the integral equation K g(t) _dt = 1 Vx-t…

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Q: Evaluate the integrals in Exercises 17–66. V3 – 2s ds 17. 18. ds V5s + 4 fovT 20. / 3y V7 – 3y² dy…

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Q: Refer to V=C[0,1], with the inner product given by an integral. Compute (f.g), where f(t) = 16t – 12…

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Q: 3. Evaluate the integral: = Im z°dz, C: =1 (-x< Arg I<)

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Q: Compute the double integral of f(x, y) = 12x³y over the given shaded domain D. /| 12x³y dA = 2 1 2 3…

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Q: 22. Evaluate the iterated integral. (b) f. [, 2x + »)'dy (a) x+y+ xy dydx

A: Now we will solve the given double integral  We know integration of Xn dx = X(n+1) / (n+1) + C ,…

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: evaluate the triple iterated integral.

A: Integrate with respect to r first

Q: 2- Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

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

A: Given :∫12∫1x∫y2lnyz dz dy dx=I

Q: H.W: Evaluate the integral: VE 3y 8-x2-y? 1. dzdxdy 0 0 x2+3y2

A: Formulae used:

Q: 11. Show that the quotients field of the integral domain Z[i] = { a+ib: a, b e Z} is K={x+iy: x, ye…

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Q: Calculate the integral f. (z-2)²2 dz, where C: |z – 1| = 3.

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

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: y 3 2-…

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

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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: Evaluate the triple integral f (x, y, z) dV. S (x, y, z) = x² + y4, Q = {(x, y, z) | 0<x<2,…

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Q: 1- Assume that x, y E R and z = x + iy E C .Calculate the following integrals using the given…

A: Note: According to our guidelines We’ll answer the 3 subparts of the question since the exact one…

Q: Evaluate f z2 In z dz using integration by parts O 22 In z – +c 12 O In z - +c O 22 In z-폭 +c O In z…

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Q: xdx The evaluation of the improper integral is .2 - - 6. C 6 C None of these MacBook Air 116

A: Substitution method

Q: 1-) Assume that x, y E R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Suppose that f(x, y) = √√/4² -2² - y² on the domain D = {(x, y) | x² + y² ≤ 4²}. Q Then the double…

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Q: 2. Evaluate the improper integrals of (a) In r dr OP -2 (0 + 1)³/5 (c) / re dr 4 dr (4) L r² + 16

A: To find - Evaluate the improper integral of    Formula used - Integration by parts :

Q: b)compute the I = dz integral the c こ belo w (Zり2 1ver em (2) 2i Re (2) -2i

A: The given integral is  I=∮c1z2+42dz Clearly, the integrand has two singularities that is z=2i  and…

Q: Evaluate the triple integral of defined by z > 4. f(x, y, z) = z(x² +y? + z?)-3/2 over the part of…

A: Converting the triple integrals to spherical coordinates, we have; f(ρ,ϕ,θ)=ρcos(ϕ)ρ^{−3/2}\\…

Q: Evaluate the integrals in Exercises 9 and 10. 9. 8x sin y de – 8y cos x dy C is the square cut from…

A: Explanation bye green's theoram in plane, we have  ∫∫R(∂N∂X-∂M∂Y)dxdy = ∮Mdx +Ndy compare the…

Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y² ≤ 4}. I Then the double integral of f(x, y) over…

A: Explanation of the answer is as follows

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

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Q: 1-) Assume that x, y € R and z = x + iy e C and answer the followings. Calculate the reel integrals…

A: Given: (a) ∫-∞∞ x2x4+1 dx (b) ∫-∞∞ x2(x2+1)2 dx We have to calculate the (a) and (b)

Q: Evaluate the triple integral of f(x,y, z) z(x2 + y? + z²)-3/2 over the part of the ball x² + y² + z²…

A: please  see the next step for solution

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: Which of the symbols below denote the operation of antidifferentiation? c. Sf(x)dx = F(x) A. F(x)) =…

A: Since, you have posted 3 questions. We"ll solve first two questions, because 3rd one is incomplete…

Q: a) Evaluate the double integral MUTM 1 UTMO dydx. x²+ y? ITM UTM

A: The given integral is ∫02∫01-x-121x2+y2dy dx

Q: 1 -de is not an improper integral z +1 Select one: O True O False

A: We need to know the definition of Improper fraction to solve this

Q: | Fug kuote the triple integral SSS 3ydv, where =L(ay.) | os xE2, 0sys lu-x?, 0s2sx.

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Q: Suppose that f(x, y) D = {(x, y) | x² + y² < 9}. 6, and Then the double integral of f(x, y) over D…

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Q: Compute the double integral of f(x, y) = 18xy over the given shaded domain in the following Figure :…

A: Given fx,y=18x5y

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

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Q: Suppose that f(x, y) = 6, and D = {(x, y) | x² + y? < 4}. Then the double integral of f(x, y) over D…

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Q: Evaluate the triple integral: A 24 B 6 12 18 √₁³√₁² √²(x + y + (x+y+z)dydxdz

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Q: Suppose that f(x, y) 5² – x² – y² on the domain D = {(x, y) | x² + y² < 5²}. = tr=5 Then the double…

A: Here we have to find the double integral of the give function in the given domain.   Convert the…

Q: Compute the double integral f[148 sin( + ) oyck, where R = {(x,y) /0 5x s %,0 sy s }. х, 3J. R OA…

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Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: Sds, C: rt) = (3r², r?), tel1,3] Which one of the following "regular" integrals represents the above…

A: Given: ∫Cxy3dS, C:rt=3t2,t2 ,t∈1,3