(b) Given that the integral of a function تی- قو-4/ zV² + y² + z² dzdxdy i. Sketch the projection, R on the æy-plane and the solid of integration, G for the integral. ii. Convert the given integral to an equivalent multiple integrals in the spherical coor- dinates. iii. Hence, evaluate the given integral.

Q: 2. VI-x² !! 1 dy dx- dz 0 -1V1-x2

A: Change Cartesian coordinate to cylindrical coordinate by using x = r cos(theta) y = r sin(theta) z =…

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Q: Evaluate the integral by changing to cylindrical coordinates. 16 - y2 xz dz dx dy 16-y2 Vx2+

A: The given integral is                      ∫-44∫-16-y216-y2∫x2+y26xz dz dx dy

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A: Given semicircle x2+y2=R2,  y≥0 The figure of this semicircle is shown below. In the above figure,…

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A: According to the given information, it is required to solve the triple integral.

Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

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Q: ローペープ 8-x²-y z?dzdxdy. Use cylindrical or spherical coordinates to evaluate the integral.

A:

Q: 29–30 Evaluate the integral by changing to cylindrical coordinates. '2 V4-y² 29. xz dz dx dy |-2…

A: To evaluate the below integral using the cylindrical coordinates. ∫−22∫−4−y24−y2∫x2+y22xzdzdxdy

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A: Given that density = x + 2y + 4 and rectangular plate is bounded by the lines y =1 and x = 6

Q: Evaluate the integral by changing to cylindrical coordina xz dz dx dy -2J-/4-y² x+y²

A: Introduction:   Let f(x,y,z) be a three-variable continuous function defined over a solid Q. The…

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A: We have to evaluate the given integral.

Q: F(x, y, 2) = xi + yj + 9k, s

A:

Q: Integrate f(z) = (7)° counterclockwise around the unit circle, using Cauchy's integral theorem if…

A: using cauchy residue theorem to find given integral...

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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 integral by changing to cylindrical coordinates. xz dz dx dy V4- ya Vx² + y2

A: We will solve the problem.

Q: 11. change the iterated integrals to cylindrical coordinates V9-x? zydzdydx Зл 9-r2 JT zr? sin…

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Q: V4-y² 4-x²-y² LL" L +yi + z°dzdsdy -2 Jo /4-x²-y²

A: Consider the given information: ∫-22∫04-y2∫-4-x2-y24-x2-y2y2x2+y2+z2dzdxdy To calculate integral by…

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Q: Set up an iterated triple integral equal to 3 3-x² x²+y² 3 2-√4-x²-y² using: Spherical coordinates…

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Q: Which of the following is the triple integral for the function f(x, y, z) = (x² + y² + z²)³ bounded…

A: using spherical coordinate

Q: Write the integral x* dz dy dz in cylindrical coordinates. DO NOT EVALUATE THE INTEGRAL!

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Q: Use spherical coordinates to evaluate the integral •√₁-x² √√₁-x²-x² (x² + y² + ²)dzdydx.

A: To evaluate the integral using spherical co-ordinate system :-

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Q: Use cylindrical coordinates to evaluate the integral 2 /2x-x x²+y? 2 2 s Vx´ + y´ dzdydx 2 -V2x-x

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Q: Convert S.S. dzdydx 3-√√9-**-* Into an integral of spherical coordinates 319-x2

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Q: Evaluate the integral by changing to cylindrical coordinates. 25 – y2 '5 '5 xz dz dx dy x2 + y? 25 -…

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Q: Evaluate the integral by changing to cylindrical coordinates. 16-1 c16-r² -y? Vx2 + y? dz dy dx =…

A: Given: The given integral is, ∫-44∫016-x2∫016-x2-y2x2+y2dzdydx. The objective is to evaluate the…

Q: Evaluate the integral by changing to cylindrical coordinates. 16 - y2 xz dz dx dy 16 - y2 x² + yZ

A: Here, the given limits are z=x2+y2   to   z=7. Put x2+y2=r2 implies, z=r The limits of z in…

Q: . Express the area of the portion of the paraboloid z=x² + y? that is above the xy plane and below…

A: Asked questions is solved.

Q: Express the double integral || (x +1)dA, where 2 is the region in the upper half- plane (i.e. y20)…

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Q: valuate the following triple integral by using spherical coordinates. V16-x2 32–x²-y² (3x² + 3y² +…

A: The integral can be converted from a rectangualr coordiane system to the spherical by using the…

Q: (b) Evaluate the following triple integral by using spherical coordinates. 16-x2 32–x²-y2 I = (3x² +…

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Q: To find the arclength of y 3x2 +4 from r 0 to z 4, which is the correct integral? OL = V1+6z dx OL =…

A: Weknow that arc length of the curve is ,L=∫x=ax=b1+[f'(x)]2dxTherefore arclenth of y=3x2+4 from x=0…

Q: 8. Consider 4-a2-y2 azdz da dy Jo (a) Write the integral in cylindrical coordinates. (Do Not…

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Q: 4. Convert the following triple integral into cylindrical coordinates (Do Not Evaluate). 16-r2…

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Q: Consider the integral 2zx? dx dy dz, where N is the domain bounded from below by the cone z = by the…

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Q: tes to evaluate the triple integral e Vz² + y² + pounded by the spheres z² + y² + z² = 4 and z? + y…

A: Given, ∫∫∫Ee-x2+y2+z2x2+y2+z2dV E is the region bounded by spheres x2+y2+z2=4 and x2+y2+z2=25.

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Q: Evaluate the following line integrals. Do not resort to parametrization, but instead use an…

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Q: Set up an iterated double integral in polar coordinates equivalent to the area of the surface on the…

A: You asked for the surface below z=2, not bounded below by plane z=2,

Q: Evaluate the following integral with the help of cylindrical coordinates /25–x² •125 3/2 (x² +…

A: We have to evaluate the integral using polar coordinates