Evaluate the double integrals: J| (x+ y+1)dxdy

Q: Evaluate the iterated integral. 24 (x + y + z) dx dz dy of

A: To find: ∫02∫04∫01x+y+zdxdzdy

Q: 2x Evaluate the improper integral J da, if it exists. (z² + 121)?

A: Use the substitution method of integration

Q: Evaluate the double integral. dA, x2 + 1 {(x, y) | 0 < x < 2, 0 < y < Vx}

A: We are clearly given the limits of the integral. Since y limits are in terms of x so dA = dy dx

Q: Evaluate the double integral / (a (x² ,2 + 8y) dA, where D is bounded by y = x, y = x°, and x > 0.

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Q: Express the integral in terms of the variable u, but do not evaluate it. In x dx; u = In x e2 In x…

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Q: Evaluate the iterated integral by choosing the order of integration. e( 4x In(y) Зy In(x) dy dx

A: We have to compute the double integration

Q: Evaluate the integrals in Exercises using integration by parts.

A: The integral given to us is  ∫y16-y2dy

Q: dw V5 – e-2

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Q: Calculate the integral $dz, where C: |z] = 2.

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Q: Evaluate the double integral (x² + 2y) dA, where D is bounded by y = x, y = x³, and x ≥ 0.

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Q: Calculate the double integral where R = [1,2] × [-1,1]: R xeᎩ dᎪ

A: Sol:- It can be re-written as :- ∫12∫-11xeydydx......................(1)First siolve this…

Q: Evaluate the double integral. 8ху? dA, D is enclosed by x = 0 and x = 4 – y2

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Q: Evaluate the double integral x° dA, where D = {(x, y) : 1 < æ < e,0 < y < In x}.

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Q: Evaluate the integral p.v. J e2ix -dx. 00 x+1

A: We can apply Cauchy integral theroem to find the integral.

Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

Q: Evaluate the integral. r 81 In(y) dy Vy 64

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Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 <x< 3, 0 sy s Vx} ID

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Q: Evaluate the double integral. dA, D = {(x, y) | 0 < x < 9, 0sys Vx} ID x² + 1

A: The double integral is given by:

Q: Evaluate the double integral x cos y dA, where D is bounded by y = 0, y = x², and x = 5.

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Q: Define the following improper integrals integral a to b f(x) dx

A: Let F'(x)=f(x) then,

Q: 7 dx. J 2+ Vx – 4

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Q: Evaluate the double integral x cos y dA, where D is bounded by Y = 0, y = x², and x - 2. Answer:

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Q: Use Romberg integration to compute R3.3 for the following integral x sin x dx

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Q: Change the order of integration in the following integral /| f(x, y)dydx.

A: To change  The order of integration.

Q: Extend your knowledge of double integrals to evaluate the triple integral So So S**** f(x, y, z) dz…

A: Given that I=∫01∫0x∫01+x+yf(x,y,z) dzdydxTo extend the double integral to triple integral.

Q: Evaluate the integral. inegral  1 / (x+a)(x+b) dx

A: 1x+ax+b=Ax+a+bx+b   →1 On simplification, we get ⇒1x+ax+b=Ax+b+Bx+ax+ax+b⇒1=Ax+b+Bx+aNow when x=-a,…

Q: Evaluate the integral.

A: Given, ∫49lnyydyLet, I=∫49lnyydy Integrate by parts we get,…

Q: Evaluate the double integral || (x2 + 4y) dA, where D is bounded by y = x, y = x³, and x 2 0.…

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Q: Evaluate the double integral æ cos y dA, where D is bounded by y = 0, y = x², and a = 1. Answer:

A: Solve the following double integral

Q: Evaluate the double integral. бу dA, 2x5 + 1 D = {(x, y) | 0 <x< 1, 0 < y s x²}

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Q: Evaluate the improper integrals: (a): xe ,-x dx •4 dx (b) V4-x

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Q: Evaluate the iterated integral. •x5 V 64 – x6 dy dx /o Jo

A: The given integral is:∫02∫0x564-x6dydxWe need to evaluate the integral.

Q: evaluate the iterated integral.

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Q: ∙1 Ꮭ ᏝᎽ 1-x-y z dz dy dx

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Q: Evaluate the double integral x° dA, where D = {(x,y) : 1 < x < e, 0 < y < In x}.

A: Evaluate the double integral as follows.

Q: Evaluate the double integral Jo J-y? dxdy

A: To evaluate: ∫02∫-4-y20dx dy

Q: Evaluate the double integral (x2 + 8y) dA, where D is bounded by y = x, y = x°, and x > 0.

A: Value of the given double integral is 71/84

Q: Evaluate the integral, 00 xn+1e-a²x* Jn(bx)dx, a > 0, b> 0,

A: Bessel's function of first kind of order n, denoted by Jnx is defined as Jnx=∑r=0∞-1n22rr! γn+r+1x2r…

Q: Evaluate the double integral. IL sy? da, D= {(x, y) I -1 s y s 1, -y – 2sxsy}

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Q: V 11y2 – 15 dy y2

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Q: Evaluate the double integral ∬D (x2+2y)dA , where D is bounded by y=x, y=x3, and x≥0.

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Q: O Evaluate the integrals Jscx+y+2?s da dy dx-

A: according to the guidelines we should have been able to do only one question at a time #1-a

Q: The improper integral J 1 r2-4x-5 dx is given by:

A: In this question, we reduced the integral into trigonometric form by using suitable transformation.

Q: Compute the double integral of f(x, y) = 45xy over the domain D. D: bounded by x = y and x = y2 45xy…

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Q: Evaluate the double integral (x2 + 6y) dA, where D is bounded by y = x, y = x³, and x > 0. Answer:

A: We have to find the value of the integral

Q: Evaluate the double integral x* dA, where D = {(x, y) : 1 < x < e,0< y< In x}. %3D

A: The solution is given as

Q: Evaluate the double integral. dA, D = {(x, y) |0Sx< 5,0 < ys Vx} x2 + 1

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Q: Evaluate the double integral J[₂x² x³ dA, where D = {(x, y) : 1 ≤ x ≤ e, 0 ≤ y ≤ ln x}.

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Q: The improper integral dx is (x+2)S

A: