33. Average height of a hemisphere Find the average height of y² above the disk the hemispherical surface z = Va² - x² + y² ≤ a² in the xy-plane.

Q: 2z tan a (1+ tan? z) dz

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Q: 2πT 1 I₂ = So dt. 13 + 5 cost Let I be the unit circle {z e C : |Z| = 1} parametrised in the…

A: Solution:Let z=eιθThen z=cosθ+ιsinθ (By Euler's…

Q: . A donut with major radius R and minor radius r can be represented parametrically by r(u, v) =…

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Q: 7. Set up the integral in polar form that gives the area of the surface formed by revolving the…

A: We have to set up the integral in polar form such that the area of the surface formed by revolving…

Q: 1.5 3-y QI) Evaluate the integral dx dy using polar coordinate

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Q: When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I…

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Q: Bernoulli's equation: Q: dy don + m Sinzy = nicorty Herce, Plw) = e Noww by dividing both sides by…

A: The differential equation of the form, dydx+P(x)y=Q(x)yn is called as Bernoulli's differential…

Q: Evaluate the following integral In 3 √(In 3)²-y² 0 0 eV x² + y² dxdy

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Q: 3 Evaluate the integral cos(x² + y²)dydx by converting to polar coordinates 0 0

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Q: Compule he an Curvc given aM byO x= and ye 3tcos(t) 'from DLtL engh ot M pacbmeter 3t Sin (t)

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Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

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Q: Q.1) Use the polar integral to evaluate 1-(z-1)2 I+y

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Q: Find div F and curl F if F(x, y, z) = xz°i+ 4y°x*j+22²yk. div F= curl F=

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Q: For the rose r = 4 sin(20) and circle r = 2 shown in the figure. Find the area inside the rose and…

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Q: Q.1) Use the polar integral to evaluate 2 dydr 71+ Vr2 + y?

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Q: C: x² + 4y² = 4; z = 1 R(t) = (2 cost, sint, 1), t = [0, 2π]

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Q: Integrate (2)dz, C: clockwise unit circle centered at (0, 0).

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Q: (z -1) (z+2z -3) Q1/ Find the value of the integral dz, where y is the triangle with Vertices at the…

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Q: The path integral v. dr, where v = direction) is given by (sin y, r- cos y) and C is the perimeter…

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Q: owing integrals using Polar © SSx dzdy Sydydx -dydz 1+V+y -Vi-2

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Q: √1-y² If ²₁¹² x² + y² dxdy is changed to equivalent integral in polar coordinates, then the…

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Q: Q3) For the following function: 1 U= zlog(x² + y²) 1. Determine whether it is harmonic (satisfy…

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Q: (8. e Sin y Ausi Sin 2

A: Solution is written in below steps.

Q: QI) Evaluate the integral dx dy using polar coordinate

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Q: 3. Determine order and degree of d³y ;+ sin (y") = 0 dx*

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Q: 3. (ey + 1)²e-dx + (ex + 1)³e¯*dy = 0

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Q: # 2. So sin 32 dz C: Izl=3 (z-5)

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Q: (0,27,2x) (0,21,0) In the figure above, the path C is shown as the part of a helix given with…

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Q: ply) = secly) + e ² Find p'ly)

A: Solve for the derivative