Find M.and (x, y) for the laminas of uniform density p bounded by the graphs of the equations.y = Vx + 3, y =My(x, y) =

Answered: y = Vx + 3, y =x + Mx My (x, y) =

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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Question

Find M.
and (x, y) for the laminas of uniform density p bounded by the graphs of the equations.
y = Vx + 3, y =
My
(x, y) =

Expert Solution

Step 1

For calculating these values we have to calculate an area and for that we have to plot a graph. First calculate the area of the common region between two curves. After that calculate the moments about x and y axis then use these result to calculate $(x, y)$ .

Moment about x axis that is $M_{x}$ is defined as $M_{x} = ρ \int_{c}^{d} [\frac{f (x) + g (x)}{2}] [f (x) - g (x)] d x$

Moment about y axis that is $M_{y}$ is defined as $M_{y} = ρ \int_{c}^{d} x [f (x) - g (x)] d x$

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