Question2:xeya. Using Polar coordinates Evaluate - y dx dy2y-b. Find the center of mass and the moment of inertia about (I,) of a lamina bounded by:y = x, y = 0, y = 1, x = 3 where the density function p(x, y) = 4x + 3yc. Evaluate y ? (2x - y) e dx dy with y = v, x = u+

As you didn't mention the question numberto be solved so i solved First 2 question.For remaining…

Answered: 2y-y y dx dy a. Using Polar coordinates…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose a laminar region with shape x2 + y2 ≤ 4 and y ≥ 0 has two dimensional density given by σ (x, y) = x2 Use polar coordinates to answer the following questions. (a) What is the mass of the above laminar region? (b) What is the center of mass of the above laminar region?
8.2 Review your line integral skills: Consider a wire in the shape of a helix r(t)=7costi+7sintj+4tk,0≤t≤2πr(t)=7cos⁡ti+7sin⁡tj+4tk,0≤t≤2π with constant density function ρ(x,y,z)=1ρ(x,y,z)=1. A. Determine the mass of the wire: B. Determine the coordinates of the center of mass: ( , , ) C. Determine the moment of inertia about the z-axis: Note: If a wire with linear density ρ(x,y,z)ρ(x,y,z) lies along a space curve CC, its moment of inertia about the z-axis is defined by Iz=∫C(x2+y2)ρ(x,y,z)dsIz=∫C(x2+y2)ρ(x,y,z)ds.
Consider a sheet S whose shape is given by the portion of the surface of equation z = 2 cos2 y + y (see figure), for which its density function is ρ (x, y, z) = y + 1. The approximate mass of S corresponds to:
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D is a region in the 2nd quadrant that is inside a circle with equation x2 + y2 = 16 and outside the circle with equation x2 + y2 - 4y = 0. Set up a double integral for the mass of the lamina in the shape of region D with density function f(x,y) = x2 - x + y2 using polar coordinates.
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2y-y y dx dy a. Using Polar coordinates Evaluate