et z e C, r>0 and a(z,r) := z + re", te [0,27]. Calculate the following integrals: a) Saça.1) dz; b) Sasi1) dz; c) Sa(-22) dz;

Q: Suppose that f(x, y) = 4, and D = {(x, y) | a² + y? < 9}. Then the double integral of f(x, y) over D…

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Q: Find the line integral of f (x, y,z) = -x + y + z over the straight-line segment from (1, 2, 3) to…

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Q: Choose five other iterated integrals that are equal to the given iterated integral. x² f(x, y, z) dz…

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Q: Evaluate the line integral, where C is the given cu curve. (x + yz) dx + 2x dy + xyz dz, C consists…

A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

Q: Evaluate the given line integral. | (y, -x) · dR, where C consists of the uppder part of x2 + y? = 1…

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Q: Use spherical coordinater to set up the integmal SzdV, the integral SSSz dV, where Q lies between…

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Q: z dV, B (x – 1)2 onde B := {(r, y, x): (y – 1)² + 22 < 2z 4

A: Here is the solution of the given problem. Volume integral:

Q: Rewrite the iterated integrals in the order dydzdx 11-z- 1-z SS S f(x,y, z)dxdydz

A: Let's find.

Q: Prove from the definition of the Ito integral that sdW, = tWt – | W,ds.

A: To prove the below statement using the definition of integration. ∫0tsdWs=tWt−∫0tWsds

Q: Express the triple integral by using cylindrical COordinotes. SSSR (6+x+y) dV where R is bounded…

A: Take projection on to xy plane and use the cylindrical coordinates dV=r dr dt dz

Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: Rewrite the iterated integrals in the order dzdydx 11-y? 1-y SS S f(x,y, z)dædzdy So So" o f(z, y,…

A: Please refer to the image below

Q: Evaluate the line integral, where C is the given curve.     C xeyz ds, C is the line…

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Q: 6. Use Green's Theorem to show that the area of the unit disk x2 + y? <1 in R? is T by evaluating a…

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Q: Use Green's Theorem to evalute this integral where C is a triangle with point coordinates (0,0),…

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Q: Evaluate the following line integral (x + y)ds where C consists of line segments from (0,0) to (9,…

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Q: Compute the following integral: ez -dz z(z – 3) where y = {z : |z| = 2} positively oriented.

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Q: H I Evaluate the integral, --) dV where, E lies between spheres z +y + z = 1 and ² + y² +z? = 2, for…

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Q: Find the line integral of f(x,y,z) = -x+y+z over the straight-line segment from (1, 2, 3) to (0, −1,…

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Q: The value of the triple integral J.J.J v+2z)dzdydx (Correct to ONE decimal place) will be

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Q: Sketch the curve ĕ= E Set uf, buz de not evaluale, an integral for the are- length of the Rurve from…

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Q: compute the given double integral over the indicated rectangle. // by a – 2y° dA R= [1,4] × [0, 3] R

A: Given Integral: I=∬R(6yx-2y3)dA dA=dx.dy R=1,4×0,3 Limits of x are from 1 to 4. Limits of y are from…

Q: 2. Compute the line integral of f(r, y) = r over the curve C, where C is a triangle formed by…

A: Now we have to find the line integral: ∫C x dswhere C is triangle joining the points:  (0, 0),  (1,…

Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: Rewrite the iterated integrals in the order ddzdy 11-z 1-z SS S f(1,y, z)dydzdr

A: ∫01∫01-z2∫01-zf(x,y,z) dydzdx To Find: Rewrite the integral in the order dxdzdy.

Q: Find the line integral of f(x,y,z) = -x + y+z over the straight-line segment from (1, 2, 3) to (0,…

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Q: Evaluate the triple integral 2xe" sin z dV, where Q is the rectangle defined by Q = [(x, y, z)| 0…

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Q: sin(z) Sc (3z – 2)(z – 3) dz

A: Please find attachment for the

Q: 21. (y² dx + x² dy)

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Q: Which of the following is a valid triple integral? -Зу O f S"L* 3 dydzdx +y? O L* L*** 3 dzdydx 0.…

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Q: Suppose S is the cylinder parametrized as follows: Set up a double integral that represents the…

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Q: Evaluate the given line integral. | (y, –x) · dR, where C consists of the uppder part of x² + y? = 1…

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Q: Use Cauchy's Integral formula to evaluate the integral: Sa (z+1) e2z dz where C is a circle |z| = 3.…

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Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

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Q: Evaluate the line integral In(x + y) ds, z + 2 where C is the line segment from the point (1,0, –1)…

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Q: 7. Use Green's Theorem to compute the line integral | ry? dx – x² dy, where C is the triangle with…

A: ∫xy2dx - x2dy triangle vertices are (0,0), (2,0), and (2,2)

Q: Evaluate the integrals in Exercises 23–26. TT 23. cos (x + y + z) dx dy dz 0 Jo Jo -In 7 cln2 cIn5…

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Q: Evaluate the double integral | 3xydA where Ris bounded by y=2– x, y=0, and x =4 –-y² in the first…

A: this problem is related to application of integration

Q: Use green's theorem to calculate the integral Fdr, F(x, y) = (e* + a²y , e" – xy² + sen(y) + 2)…

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Q: Which one of the iterated integrals below are equivalent to dy dz? (There is a penalty for incorrect…

A: Given: ∫-11dy∫y21dx∫01-xdz To Find: The correct iterated integral for the above given integral.

Q: Evaluate the integral: (In z)6 dz %3D

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Q: Evaluate the iterated integral. SIT stad dy dx dz 5ze

A: Answer and explanation is given below...

Q: Find the line integral of C in two ways; A) Directly. B) Using Green's theorem. C eata formed by the…

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Q: ( b). Je2cos (πx) dx .

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Q: Compute the line integral of f = x? - y, along C:x² + y? = 4 in the first quadrant from (0,0) to…

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

Q: Choose five other iterated integrals that are equal to the given iterated integral. '2 f(x, y, z) dz…

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Q: Evaluate the integral using any appropriate In2y dy y + 8y In y In ?y dy =] %3D y+8y In 3y (Турe…

A: Given : ∫ln2yy+8yln3ydy