3. Chapter 15 Review 37: Convert to spherical coordnates and evaluate: 4-x² LENT 4 x² - y² e-(x² + y² +z²) ³/² dz dy dx

Q: spherical' covdinates in

A: Given: Orthogonal curvilinear coordinates. To Obtain: The expression for ∇2f.

Q: 2. Use cylindrical coordinates to evaluate √√9-x² 9-x²-y² [dz x² dz dy dx. √9-x2 0

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Q: Use spherical coordinates to evaluate f (ử+y° +z°)* dydzdx. 3/2

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

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Q: tind the Laplace trans form for the following 2メ f)= sinat uct) %3D +jat -jat e - e Euler idrolity…

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Q: [(VxA)• dS over the surface of a hemispherical b 2 and its circular rim if A = 3 sin()â

A: Sol

Q: O Evaluate Saxsin@8A the ufper 28sin@dA where R is the Card ioid the parabola the inside half 8= 2a…

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Q: 4. Use spherical coordinate system to find the area of the strip as0SB on the spherical shell of…

A: Given Strip α≤θ≤β on the spherical shell of radius awhen α=0 and β=π

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A: Given integral is ∫1e∫0π1xsin2(y)dydx

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Q: The area of the region inside r = 6 cos 20 the rose and outside the circle = 3/2

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Q: Graph the cardioid r = a(1+ sin®), a< 0?

A: We are given that r=a(1+sin∅), a&lt;0 Here as we know that sin∅ is always greater than equal to -1.…

Q: Q1) Evaluate the integral dy dx using polar coordinate

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Q: 3. + x° siny-y と3 cOS C fond C Frc foeと y g りな in) fy

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Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: c) h(p,g,0) = psin@cose ah sin@cos0 ; ah = pcos@cose answer: - %3D ah =-p sinøsin0 d) W(P,V,8,v.g)=…

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Q: If C is a circle of radius 7 centered at the point ( -5, -1 ), then evaluate $ (34 (3y - esin(x)) dx…

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Q: Convert x = = ln(2t) and y = 1² from parametric to rectangular form. 2

A: Given,  x=ln(2t) and y=12t2

Q: (8. e Sin y Ausi Sin 2

A: Solution is written in below steps.

Q: c.) 3 (1+1) dy = 2ry (y" – 1) dz d.) (z+1) +(* +2) y = 2ze e.) 2y dy - (3y cot z+ sin z cos z) d

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

Q: Show: 2 x + 2 sin dydx + 2y 1 va sin-dydx = 4 2y 2 va

A: The question is of change of order. First we need to identify the region formed by limits of…

Q: c) Use spherical coordinate to evaluate V1-x2 1 Vx2 + y? + 22 dz dy dr.

A: The given problem is to evaluate the given triple integral using spherical coordinates, we have to…