23. Evaluate II (x² + y? + z²)² dV, where B is the ball with center the origin and radius 5.

Q: 2. Use Green's Theorem (and only Green's Theorem) to evaluate |(2? + y)dx + (x² – y³)dy, where C is…

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Q: (15) Let D be the half-disk x² + y? 0. Compute / | (a + y) dA D

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Q: 1 in 1in y 1 in 3 in 1 in X

A: Consider the diagram and divide into four regions as shown below, Now, make a chart and evaluate…

Q: Evaluate J₁ 1 E x² + y² + z² x² + y² +2²= 25 in the first octant. dV, where E lies between the…

A: Here we need to use spherical co ordinate system to find value of integral  Relation between…

Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: 7. Evaluate * SS $6(x² + y² + z?)dV B where B is the ball with center at the origin and radius 1 8л…

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Q: Let B be the ball with center at the origin and radius 1 SS $3(x² + y? + z²)dV = B

A: Solve integral by using Cylindrical cordinates

Q: Q4) Using Green's theorem to evaluate: (12 marks) Sc [ (x3 – xy³)dx + (y³ – 2xy) dy] Where C is the…

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Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and %3D x? + y? + z? = 4 in…

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Q: Evaluate ze*²+y²+z? dV, where E is the portion of the ball centered at the origin of radius 5, x2 +…

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Q: 17. Use sphtrical coordinates. Evaluatc ||ry)dV, where E O lies betueen the spheres X'ty +Z²=1 and…

A: The relations between the cartesian and spherical coordinate system are x=rsin(θ)cos(φ),…

Q: Evaluate //. dV, where E x2 + y² + lines between the spheres x + y + z? and x + y? + z2 = 25 in the…

A: Consider the provided question, Evaluate ∫∫∫E1x2+y2+z2dVwhere, E lines between the sphere x2+y2+z2=1…

Q: What's the probability that the point (that is chosen at random from the unit cube) lies below the…

A: The figure is as shown below:

Q: Let B be the ball with center at the origin and radius 1 SS [3(x² + y² + z²)dV =

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Q: Evaluate ſ[ſp z dV where E lies between the spheres x² + y² + z² = 1 and + y*¨+ 2² = 4 in the first…

A: Solution:

Q: 1 Evaluate dV, where E lies between the spheres x + y + z = 16 and + y? + z2 = 64 in the first…

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Q: 18. Evaluate § (9 − x² − y²) dV, where H is the solid hemi- sphere x² + y² + z² ≤ 9, z ≥ 0.

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Q: 2. Find the area of the part of the surface z = cylinder x2 + y² = 9. 3xy that lies within the

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Q: Evaluate the following. dV where R is the portion of the ball of radius 1 in 4-dimensions with all…

A: We need to evaluate the value of integral in 4 dimensions.

Q: Let B be the ball with center at the origin and radius 1 SSS 4(z² + y² + z²)dV = B

A: Explanation of the answer is as follows

Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

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Q: 1. Find the area of the part of the planer+ 2u + 3z = 1 that lies inside the cylinder x2 + y? = 3.

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 +y? + 2? = 1 is T =…

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Q: Let B be the ball with center at the origin and radius 1 3(x² + y + z?)dV = %3D B

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Q: # 4. Evaluate the line integral | (x +2x²y) ds, where C is the upper half of the unit circle x2 + y2…

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Q: Let B be the ball with center at the origin and radius 1 SS S2(z² + y² + z²)dV = %3D 8M 16x 5. 24x

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Q: 23. Evaluate II (x² + y² + 2²)“ dV, where B is the ball with center the origin and radius 5.

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Q: where B is the ball with center at the origin and radius 1

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Q: (a) Compute the area of the portion of the cone x2 + y2 = z? with z 2 0 that is inside the sphere x2…

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Q: 18. Use spherical coordinatcs Evaluate dV,where E is the portion of the unit ball X ty +z²<! that…

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Q: 1 Evaluate dV, where E lines between the spheres a? + y? + z² = 25 and %3D x² + y? + z2 49 in the…

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Q: D be the region that consists of points (x, y) such that x² + (y - 3)² ≤9. Then, (x² + y²) dA equals…

A: see my solution

Q: Let B be the ball with center at the origin and radius 1 I//3(x² + y + z?)dV =

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Q: 22. Evaluate xyz dV, where E lies between the spheres p - 2 and p- 4 and above the cone - 7/3.

A: Solution:-

Q: 12- Evaluate JJI (x2 + y? + z?)dvwhere B is a ball with center the origin and radius 5. B

A: Given problem is :

Q: Let B be the ball with center at the origin and radius 1 SS f6(n² + y² + z² )dV

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Q: Evaluate ([(3xi +2yi)-d$ -d$ where S is a sphere x +y +z? =9.

A: To evaluate the below integral. ∫∫S3xi+2yj⋅ds Here S is a sphere x2+y2+z2=9

Q: Jraen fusk hon conespaaday to o d'u z ul) = flx). dx² Find the the egualido for conespoodiang to…

A: Given differential equation is d2udx2+u(x)=f(x)                   (1) boundary conditions are…

Q: 16. Evaluate * :- S S $6(x² + y² + z? )dV В where B is the ball with center at the origin and radius…

A: (16).  We have to find the integral∫∫∫B 6x2+y2+z2 dV  ;      where B is the ball with center at…

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and x2 + y? + z? = 4 in the…

A: To find- Evaluate ∭Ez dV where E lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4 in…

Q: 47. Find the distance between the spheres x? + y² + z² = 4 and x? + y? + z? = 4x + 4y + 4z – 11.

A: The equation of the spheres are given:

Q: Evaluate [[[ =*dxcydz over the sphere x +y² +=² =1.

A: to find:- to evaluate the given integral.

Q: Evaluate ||| Vx² + y² + ²²&V where S lies above the cone z = Vx² +y° and between the spheres x + y…

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Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: 1. Evaluate ſſ, y dS where S is the portion of the cylinder 4x² + 2y² = 16 %3D that lies between z =…

A: Given S is portion of cylinder 4x2+2y2=16 that lies between z=0 and z=7. Parametrize the surface s.…

Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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

Q: 35. Above the cone z = a² + j? and below the sphere x² + y² + z² = 1

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Q: 1 Evaluate dV, where E lies between the spheres a? + y? + z² = 16 and E x2 + y? + z2 x? + y? + z?=…

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Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

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