3z3+2 Find the value of the integral Jc eD491dz taken counter clockwise around the cicle (a) |z – 2| = 2 and (b) |2| = 4.

Q: Q₁) Find Jz dz 1. along the contour integral c from 1+i directly to 3+i3? 2. along line from 1+i…

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Q: Evaluate the double integral I2 = || v?dzdy T where T is a triangle with vertices (-2, 0), (0, 3),…

A: Here we have to evaluate the given double integral where T is a triangle with vertices…

Q: se trapezoidal rule to estimate the the integral. V+ 4dx n=6 2.75 b) 8.53 c) 9.76 7.15

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Q: Calculate the double integral. /| 10(1 + x). 1+ y? dA, R = {(x, y) | 0sxs 3, 0 sys 1} %3!

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Q: Find what value of c does ∫∞7c/x^3dx=1 (integral is from 7 to infinity)

A: find what value of 'c' does∫7∞cx3 dx = 1taking integration on left sidec x-3+1-3+17∞   = 1c -2(x2)7∞…

Q: raluate the double integral R 3ædA where Ris the triangle with vertices (-1,0), (0,1) and (1,0).

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Q: Evaluate the integral (x2y? +y?z² +x²z²) dzdydx Maximum file s • Files

A: we have to evaluate the integral

Q: Evaluate the line integral -ydr + rdy along the curve C : y² = 6x from (6, 6) to (0,0). NOTE: Enter…

A: The given line integral is ∫c-ydx+xdy along the curve c: y2=6x from (6,6) to (0,0)

Q: y²dy (y²+16)3/2

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Q: /4-z² Rewrite the integral , L2 S* f(x, y, z)dydzdx: as an equivalent iterated integral in the order…

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Q: The improper integral da is given by: Az-5 Select one: sec((b-2)/3) O a. 1 lim 3b 100 soc(4/3) Csc 0…

A: The given proper integral is;  I=∫6∞1x2-4x-5dx

Q: The sum 5 f(2) dz + [ " f(2) dz - [, (=) dz can be written as a single integral in the form f(x) dz…

A: Please refer the attached image for complete solution.

Q: Use substitution to change the integral SS(3x + 4y)dA over the parallelogram with corners (0, 0),…

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Q: D. Use double integration to find the area of the region R enclosed by the parabola y = 4-x² and the…

A: Let's find area by using double integration.

Q: Area = 2c 27 dx

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Q: Find the area of the part of the eircle r-4 sin that lies within the sector 0 50s 87 -2/3 3 + V3 3.…

A: It is given that,r=4sinθ, that lies within the sector 0≤θ≤π3we have to find the area of the part of…

Q: 2 (2y-y² a 15. Evaluate the integral / / |zVx² + y²dzdrdy by using cylindirical coordinates. 0 0

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Q: +4)(v² +®y)Vy? +8y – 1 dy 3.

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Q: Calculate the double integral of f(x, y) = 5 – 8x over the triangle with vertices O = (0,0), A =…

A: Topic:- Application of integration

Q: Use symmetry to evaluate the double integral. 2xy J63 JR 1 + x ,10 dA, R = {(x, y) | -4 ≤ x ≤ 4,0 ≤…

A: Consider the given double integral, ∫∫R2xy1+x10dA, where R=x,y-4≤x≤4, 0≤y≤1. Consider the integrand,…

Q: Calculate the double integral of f(x, y) = 4 – 8x over the triangle with vertices 0 = (0,0), A =…

A: Consider the function: fx,y=4-8x To sketch the triangle with vertices O (0, 0), A (3, 7), B (5, 7)

Q: Calculate the double integral of f(x, y) = 2 – 8x over the triangle with vertices O = (0,0), A =…

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Q: dy Evaluate the integral| 2. y - 14y + 65

A: We first complete the square in the denominator and apply the formula:

Q: Calculate the double integral of f(x, y) = 5 – 4x over the triangle with vertices O = (0, 0), A =…

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Q: Evaluate the integral +2 zp; :- 2 in the two cases: 1) y = {z :|2| = 1}; 2) y = {z : |2| = 3}.

A: We will evaluate it by Cauchy Residue Theorem Let R be the residue then ∫f(z) dz = 2π i R Firstly,…

Q: Use symmetry to evaluate the double integral. (4 + x*y) dA, R = [0, 3] × [-3, 3] (Give your answer…

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Q: Two models, R, = 7.21+0.62t and R, = 7.21+0.47t, are given for revenue (in billions of dollars per…

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Q: Q3(a) Solve the integral below by using polar coor dinate and sketch the region 2-yt 2xy dxdy J-/2-y

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Q: Evaluate the integral 4 (y 2)(2y1) dy Jo

A: To evaluate,

Q: Use the property to estimate the best possible bounds of the integral. II. 5 sin“(x + y) dA, T is…

A: To estimate the best bounds of the integral.

Q: Solve the integral. + yz )do; o: part of the plane x + y +== 6 that lies in the first octanct.

A: Solution:

Q: Evaluate the line integral -ydx + xdy along the curve C : y? = 6x from (6,6) to (0,0). NOTE: Enter…

A: We need to evaluate the following line integral ∫C-ydx+xdy Where,  C: y2 = 6x  from 6, 6 to 0, 0

Q: tan (in |4x2|) dx is bin sec (In |(2x)ªl)| + C. what is ba The integral of A B) 4 © 1 1

A: Topic:- integration

Q: Q5 Evaluate the integrals [[(2x+y-3)dA where R is the region as shown in the figure: R (i) (ii) 1 R…

A: 5 We have to evaluate ∬R2x+y−3dA, where R is the given region. i Consider the following figure.…

Q: Evaluate the triple integral (show all your work by hand!) |T| 2.xyz dzdydx.

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Q: 2 V2y-y2 a 15. Evaluate the integral x² + y²dzdxdy by using cylindirical coordinates. 0.

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Q: Use integration by substitution to find 2ln z dr. Do not assume u = 2nz.

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Q: 2x Evaluate the iterated triple integral ſo S“ S" 2xyzdzdydx. A 5 7 8 3 8 98

A: Triple integral is used to integrate functions of three variable over three dimensional region.

Q: ASK YOU Evaluate the given integral by making an appropriate change of variables. 6. x - 8y dA,…

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Q: Use the property to estimate the best possible bounds of the integral. II 4 sin*(x + y) dA, Tis the…

A: Consider the given integral: ∫∫T4sin4x+ydA T is a triangle enclosed by lines y =0, y = 2x and x =3.…

Q: Using transform, x = V5rcos(0), y = 2rsin(0) find the product of the integral dxdy

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Q: B)Evaluate the integrals: i) it) ¹-² dxdy, 2/2 finx 2² dz dy dx.

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Q: (1,0) (1,0) 1= (x2- y?) dx + 2x y dy + i- 2xy dx + (x? - y?) dy %3D (0,1) (0,1) Calculate the above…

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Q: 2 V2y-y2 Evaluate the integral x²+ y²dzdydx by using cylindirical coordinates.

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Q: Evaluate the line integral (y dr+yrdy) taken in clockwise sense along the hexagon whose vertices are…

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Q: 8K Use Green theorem to eva luate the . line integral : 3. 3 where c is ニ thecircle

A: Given the line integral

Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

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Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

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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

Q: dz convergant 5Joj Is the Integral or divergent. I

A: